* Simplify the expression: * We can use the identities tan(x) = sin(x) / cos(x) and cosec(x) = 1 / sin(x) to rewrite the expression: sin(x) tan(x) + cos(x) cosec(x) = sin(x) * (sin(x) / cos(x)) + cos(x) * (1 / sin(x)) = sin^2(x) / cos(x) + cos(x) / sin(x) * Integrate using the formulas: * Now we can integrate each term separately using the formulas for sin(x) and cos(x): ∫ (sin^2(x) / cos(x) + cos(x) / sin(x)) dx = -∫ cos(x) dx + ∫ sin(x) dx = sin(x) - cos(x) + C Therefore, the integral of sin x tan x + cos x cosec x is sin(x) - cos(x) + C Bohot Jada Mehnat Lagi hai type karne me 😅
@@ratnajain-bs8dzbhai tum online padhte ho ya offline? Mai bhi gb sir se integration padh rha hu telegram ke lectures se and cengage illustration solve kar rha hu
mera answer root log(cosx) kyu a ra hai? btw i just started integration today, (2026tard) ky ham values ko root me calc kr skte he kya? like my thing came out to be integral of root (sec x d(cosx))
Uss sawaal me direct product nikalo aur sin square theta ko 1-cos square theta kardo Aur dusre plus wale part me niche wale cos square theta se cos theta =t lelo phir go upar uska derivative hai phir game jaisa khelke kaam tamam kardo
@@prt-tanish5547bro please guide me i am new in class 11th. Which coaching should I take How should I start preparation and which books to follow? How did you prepared. Which mistakes I don't have to do
@@UdaySingh-rn4fx mathematics me ek X ki equation ke liye infinite number of values aa jati hai to ye to algebric me hai Phir bhi kaise nikala bta deta hu Sin.tan ko sin²/cos banaya aur cosec.cos ko cos/sin banaya Phir sin²/cos me sin² ko 1 - cos² se replace kiya aur cos/sin me let sin=t krke sovle kiya aur answer agya Log|sec + tan| - sin + log|sin| + c
Bruhh Pehle stanx ko sinx/cosx likho aur for sin¢2x ko 1-cos^2x likhdo jisse eqn bnjaaegi integration of secx+cosx Second part ke lie cot theta ka integration krdo Basic formulaes Ez maths
Change tan x into sinx/cosx and cosec x as 1/sinx then ; It becomes sin^2x / cos x + cosx /sinx then: Write sin^2x as 1-cos^2x then seprate and solve and ans will be ln|secx+tanx| + ln|sinx| - sinx + c ❤
§(tanx.sinx+cosecx.cosx)dx By using formula tanx=sinx/cosx Cosex=1/sinx So we can write it §(sinx. sinx /cosx+cosx .1/sinx We know that cosx/sinx=cotx and sin^2x=1-cos^2x So §(1-cos^2x/cosx+cotx)dx §secxdx-§cosxdx+§cotxdx ln|secx+tanx|+sinx+ln|sinx|+c😅
Mene socha easy hai karte hai phir dekha to 1 ghanta lag gya phir jab dobara short dekha to pata chala vo second part cosec cos tha mene cotcosec le liya
Sir woh 2nd part easily ho jata hai.... Sirf first part ko sin and cos ke terms me likho aur fir take cos as t fir integration by parts... fir (1-t²) ko v manlo
Limit not difined hai answer alag ho sakta hai Acording to me- Int(sinxtanx)=> Int(sin²x/cosx)=> Int(1-cos²x)/cosx=> Int(1/cosx - cos²x/cosx)=> Int(secx-cosx) Int(secx) - int(cos)=> Ln|tanx +secx| - sinx+c Similarly 2nd part
Bhaiya aap iss question ko aise solve kijiye tantheta ko sin/cos break karlo aur likh do sinsquare theta /costheta then sintheta ko t man lo phir aapka expression t^2dt aa jayega phir udhar aap cosec theta ko 1/sintheta kardo wo banjayega cot theta aur ha pehle integration ko break karlena aapka answer phir ayega sin^3theta/3+ln sintheta +c 😊
dono ko alag alag integrate krlo right side wala to straight up {cotx} aur left side wala {secx} aur {-cosx} ban jayega ab bas jo bracket me hai unhe integrate krlo ans ln|secx+tanx| -sinx+log|sinx| aajaega.
Bhaiya ek question tha.. Maine 11th and 12th me jee ka kuch bhi nhi padha but mujhe ab jee krna hi hai please aap batao ki kya kru . Mai bohot chote Village se hu mujhe koi bhi guide krne wala nhi hai
To integrate the given expression, we can start by rewriting it in a more tractable form: sin(theta)tan(theta) + cosec(theta)cos(theta) = sin(theta)(sin(theta)/cos(theta)) + (1/sin(theta))(cos(theta)) = (sin^2(theta) + cos(theta))/cos(theta) = (1 + cos(theta))/cos(theta) (using the Pythagorean identity sin^2(theta) + cos^2(theta) = 1) = sec(theta) + 1 Now, we can integrate: ∫(sec(theta) + 1) dtheta = ∫(1/cos(theta)) dtheta + ∫(1) dtheta = ln|sec(theta) + tan(theta)| + theta + C where C is the constant of integration. Therefore, the integral of sin(theta)tan(theta) + cosec(theta)cos(theta) is ln|sec(theta) + tan(theta)| + theta + C.
For sinx tanx = break in sin cos, 1-cos sqaure/ sin , take sin t and alag alg solve khatam Now the next funtion break in sin cos, sin se multiply upr niche, 2sixcos=dt and sin sqaure x=t Khatam
Lekin ek minute... Chota bhai 12th mein hai isiliye integration ke questions solve kar raha aur bada bhai do saal se IIT ki taiyari kar raha hai matlab woh drop year mein hai, yeh kaise sambhav hai.
The correct answer to this question is ln(tanx+secx)+ln(sinx)-sinx+C we are taking theta is equal to x here since I don't know how to write theta in keyboard
Use by part Best method to solve integration is remember 15. Ways or type of inte. Method which ur good teacher gave u in notes Aur xam m 1 min phir last m inte ka ques ko time deena
Solution: 1.Write the expression in terms of sinx and cosx. 2.Convert all sinx into cosx using [(sinx)^2 +(cosx)^2 =1] 3.Divide and break the fraction (a-b/c =a/c-b/c) Remaining: secx-cosx+cosecx.cotx Now integrate... Answer: ln(|secx+tanx|) - sinx - cosecx + c
From chat gpt To solve the expression \(\sin\theta \tan\theta + \csc\theta \cos\theta\), let's break it down into simpler parts using trigonometric identities. 1. \(\tan\theta = \frac{\sin\theta}{\cos\theta}\) 2. \(\csc\theta = \frac{1}{\sin\theta}\) Using these identities, the expression becomes: \[ \sin\theta \left(\frac{\sin\theta}{\cos\theta} ight) + \left(\frac{1}{\sin\theta} ight) \cos\theta \] Simplify each term separately: \[ \frac{\sin^2\theta}{\cos\theta} + \frac{\cos\theta}{\sin\theta} \] Combine the fractions over a common denominator: \[ \frac{\sin^2\theta \sin\theta + \cos^2\theta \cos\theta}{\cos\theta \sin\theta} \] Simplify the numerator: \[ \frac{\sin^3\theta + \cos^3\theta}{\cos\theta \sin\theta} \] Since the numerator cannot be simplified further with common trigonometric identities, the expression \(\sin\theta \tan\theta + \csc\theta \cos\theta\) simplifies to: \[ \frac{\sin^3\theta + \cos^3\theta}{\cos\theta \sin\theta} \] Therefore, the simplified form of the given expression is: \[ \frac{\sin^3\theta + \cos^3\theta}{\cos\theta \sin\theta} \]
Subscribe karke 100k karado 🫠❤️
Secx.tanx - sinx + log|sinx| + c.
Aadhe logo ko joke hi ni smjh aaya 😂
Are ye sab toh toh chhote mote target hai aap to 10M deserve karte ho
@@asxff730galat hai log|tanx + tanx sinx| - sinx hoga
ln|secx+tanx|-sinx-ln|sinx|+c
* Simplify the expression:
* We can use the identities tan(x) = sin(x) / cos(x) and cosec(x) = 1 / sin(x) to rewrite the expression:
sin(x) tan(x) + cos(x) cosec(x) = sin(x) * (sin(x) / cos(x)) + cos(x) * (1 / sin(x))
= sin^2(x) / cos(x) + cos(x) / sin(x)
* Integrate using the formulas:
* Now we can integrate each term separately using the formulas for sin(x) and cos(x):
∫ (sin^2(x) / cos(x) + cos(x) / sin(x)) dx = -∫ cos(x) dx + ∫ sin(x) dx
= sin(x) - cos(x) + C
Therefore, the integral of sin x tan x + cos x cosec x is sin(x) - cos(x) + C
Bohot Jada Mehnat Lagi hai type karne me 😅
Respect 👍🏻
Fir bhi glt javab aaya
😂
Chat GPT Zindabaad
Ans fir bhi galat hai bro, tune kaise integrate kar diya
Mera to Log(sec(θ) + tan(θ)) - sin(θ) + log(sin(θ)) aaya
Ye 2 saal wale bhaiya me mujhe apna chehra kyun dikh raha hai😅😅😅😅😅
Us bro us 😢😢
Same bhai 😅😅
kyuki ye reel bana raha hai aur to dekh raha hai😂😂😂😂😂😂
bhai tumhara naam..............
🙂
when you realize, this is a halwa integration qn
Yes integration by parts lagega🤓🤓
No substitution lagega
@@Pwkantarpantar bhai nahi to tum pahle hi simplify kardo integration ko easily solve ho jaayega ,substitution aur ibp mein time lagega
Yes fr
@Vayu_Aksh no bro
Put that question equal to 'I' now solve 'I'
😂😂😂😂😂😂
Sin²x/cosx + cotx
So sin²x = 1-cos²x
Therefore a new expression is (secx+cosx+cotx)dx
Ab to ye baccho ka khel hai koi bhi solve kar lega
Arein pata hain bhai ....kyu Gyan jhaad raha hain@@rudranshdixit9184
@@rudranshdixit9184
Kon sa baccha integration khelta hai😢
Bhai jab itna bataya to thoda aur bata deta@@rudranshdixit9184
@@rudranshdixit9184bro mera toh integral(sec∅ + cosec∅cot∅ + cos∅)d∅ aarha hai jiska solution
ln|sec∅ + tan∅| -cosec∅ -sin∅ + C aarha h
Preparation ❎
Ratta ☑️
I'm in Motion institute, Integration topic tough hai but GB Sir ne ye topic hame bahut hi aasani se sikha diya 👍👌
Im in motion also and Ankit sir ne bhi ache se Kara diya
@@arushsharma4745 Ha Ankit Sir bhi ache hai Physics ke liye 👌👍
bhai burmen ke 90 hints dede jo sir ne class me padhaaye the
@@ratnajain-bs8dzbhai tum online padhte ho ya offline? Mai bhi gb sir se integration padh rha hu telegram ke lectures se and cengage illustration solve kar rha hu
Sahi ans hai
ln| secx+tanx| + ln|sinx| -sinx + C
Aur last me x ke jagah theata rakh Dena 👍
kar mila ye karke job mil gai?
@@abhinavgupta2885satisfaction ki tuzse ye nhi ho rha ye dekhkar
❤
Tumhe ye comment dekh kar jal raha hai?🤣@@abhinavgupta2885
@@abhinavgupta2885sukoon
Ans - ln|sinx|+ln|secx+tanx|-sinx+C
Kitne saal hogye taiyari karte hue
Wrong
Sin x + Log l sinx l + C
Isko aise bhi kr sakte ln|1-cos@|-sin@
If it had to be integrated wrt to d@
@@lostbeatz8782sahi hai mera bhi wahi aaya hai..!
This integration: 😂😂
But
Integration of √tanx : ☠️☠️
Solve this
mera answer root log(cosx) kyu a ra hai?
btw
i just started integration today,
(2026tard)
ky ham values ko root me calc kr skte he kya?
like my thing came out to be integral of root (sec x d(cosx))
@@SuccessfulInsaanTObe no wrong ans, again try
@@subhajitnath9654 im very new to integration, can u help me out?
1/2√tanx differentiation
Kal iska answer puchkar aaunga
Others : padai ka video
Me: ye bhi badminton khelta wo bhi yonex ke mehenge wale racket se😂😂
Calculus and vector algebra was my fav chapter ❤
☠️☠️
Nice taste in maths.
Nice
💀
💀💀💀
No matter where u study in the future, integration is always terrifying 😂
Bhi tumhari bat suna ki background music ki bat
Lamba ha madam lamba😂😂😅😅
Uss sawaal me direct product nikalo aur sin square theta ko 1-cos square theta kardo
Aur dusre plus wale part me niche wale cos square theta se cos theta =t lelo phir go upar uska derivative hai phir game jaisa khelke kaam tamam kardo
Ans> Log(secx + tanx) - sinx + log(sinx) +c
Bhaiya ans khali log(secx+tanx) +c hoga bs
@@atharvmishra2810 nahi bhai apna answer recheck karo.
BTW konsa saal hai prep ka?
@@prt-tanish5547bro please guide me i am new in class 11th. Which coaching should I take
How should I start preparation and which books to follow? How did you prepared. Which mistakes I don't have to do
Comments me Dusre wale bhaiya toh kuch aur answer bata rahe hai😂😂😂
@@UdaySingh-rn4fx mathematics me ek X ki equation ke liye infinite number of values aa jati hai to ye to algebric me hai
Phir bhi kaise nikala bta deta hu
Sin.tan ko sin²/cos banaya aur cosec.cos ko cos/sin banaya
Phir sin²/cos me sin² ko 1 - cos² se replace kiya aur cos/sin me let sin=t krke sovle kiya aur answer agya
Log|sec + tan| - sin + log|sin| + c
Itna bi mushkil sawal nhi h ye 😂😂😂
Abe ooi meri personal life kyu share kar rahe ho yrr mujhse puche bina case kar dunga 😂😂😂😂😂😂😂😂😂😂😂
Bruhh
Pehle stanx ko sinx/cosx likho aur for sin¢2x ko 1-cos^2x likhdo jisse eqn bnjaaegi integration of secx+cosx
Second part ke lie cot theta ka integration krdo
Basic formulaes
Ez maths
Joh integration padh raha hai usko bhi toh atleast 1.5 yrs ho gaye
ln|secx+tanx|+ln|sinx|-sinx+C
Absolutely correct
@@harshitvarshney4997yeh 12th mei ata h ya 11 th kyuki meri 11th khtm hogyi aur mujhe nhi ata plzz batado bhai😢
@@JapjotSingh-fi2it12th me 7 chapter integration me h, integration by parts, don't worry, it's easy to learn
@@RahulSharma-gv3ng thankss😅🤧
@@RahulSharma-gv3ng aur aap kya kr rhe ho 12 th mei ho?
Bro iska integration nahi hoga bcoz (dx) nhi he
Bro dtheta
Change tan x into sinx/cosx and cosec x as 1/sinx then ;
It becomes sin^2x / cos x + cosx /sinx then:
Write sin^2x as 1-cos^2x then seprate and solve and ans will be
ln|secx+tanx| + ln|sinx| - sinx + c ❤
§(tanx.sinx+cosecx.cosx)dx
By using formula tanx=sinx/cosx
Cosex=1/sinx
So we can write it
§(sinx. sinx /cosx+cosx .1/sinx
We know that cosx/sinx=cotx
and sin^2x=1-cos^2x
So
§(1-cos^2x/cosx+cotx)dx
§secxdx-§cosxdx+§cotxdx
ln|secx+tanx|+sinx+ln|sinx|+c😅
Solution: ❎
Song:✅
ans :
ln|secx + tanx|+ln|cosx|+ln|cosec2x-cot2x| - sinc +c
Wrong
The answer to this question is ln(secx + tanx / sinx) - sinx + c
Bhai ans galat hai phir se chake kar lo
Kyoki sin x भाग मे नही गुडा मे रहेगा क्योकि प्लस मे log sin x hai
Bro x ke jagah theta to tune bdla hi mhi
Bhai vo bhi glat hai ans mai log|secx+tanx|-sinx-1/sinx +c hoga
Integration by parts??
Sahi ans hai
ln| secx+tanx| + ln|sinx| -sinx + C
Aur last me x ke jagah theata rakh Dena 👍
Question was easy😂😂
Even as an 10 grader i can solve this question
Easiest question 😂😂.
Jee mai aisa aaye toh mja aa jaye dekhte hi ho jaarha pr sadly jee main itna tough aata
Yeahh I learnt integration today only and I could solve this. I'm in class 11
Mene socha easy hai karte hai phir dekha to 1 ghanta lag gya phir jab dobara short dekha to pata chala vo second part cosec cos tha mene cotcosec le liya
Bhai kyu IIT Naam kharab kar rahe ho 😅😅😂😂
Bhai dx kaha hee😂😂
dtheta
My ans is ln|secx+tanx|-sinx+ln|sinx|+c using a simple trigonometric formula and standard integration formulas
Correct ✅ ☺️
Sorry to say if you are preparing for 2 years and still couldn’t solve this sorry but you will face failure😢….
True
Bro I have succeeded to 11th in 2024 but still this question is easy for me😅😅😅
Un dono ko alag alag seperate kardo change into sin and cos form, pehle wale mein by parts laga do simply and second will change into ln form :)
log(tan ◇ + sin ◇ tan ◇) - sin ◇ +c is the required answer.
Orally kar liya 😂😂😂
ln(secx+tanx) -sinx +ln(sinx) + c
Rank kitni aayi bhai
@@bharatbihani6184 91k mains m 😓
How can you solve this without a calculator? Can someone explain step by step?
Meanwhile me a 10th grader :sin aur tan saatha mai hai toh than koh sin/cos mai change karke solve kardu
Tan x = sinx÷cosx BTW
10 grade may tune galat pad liya lgta hai
Sin /cos hota hai
mai v yhi soch rha tha baad m smjh aaya integration hai😅
Use integration by parts ;
2nd function:-tan=sin/cos
1st function :-sin
UV method is also applicable
Sir woh 2nd part easily ho jata hai....
Sirf first part ko sin and cos ke terms me likho aur fir take cos as t fir integration by parts... fir (1-t²) ko v manlo
Who is majorly focusing on song 😅
Limit not difined hai answer alag ho sakta hai
Acording to me-
Int(sinxtanx)=>
Int(sin²x/cosx)=>
Int(1-cos²x)/cosx=>
Int(1/cosx - cos²x/cosx)=>
Int(secx-cosx)
Int(secx) - int(cos)=>
Ln|tanx +secx| - sinx+c
Similarly 2nd part
aur by prts ki jagah hm direct sinx tanx ko ILATE se bhi kr sakte h but usse answer differ aayega
answer is infinity (integrand wasnt multiplied by dx)
Just use integration by parts or you can also subsitute x=pi -theta and solve fromthere
Bhaiya aap iss question ko aise solve kijiye tantheta ko sin/cos break karlo aur likh do sinsquare theta /costheta then sintheta ko t man lo phir aapka expression t^2dt aa jayega phir udhar aap cosec theta ko 1/sintheta kardo wo banjayega cot theta aur ha pehle integration ko break karlena aapka answer phir ayega sin^3theta/3+ln sintheta +c 😊
dono ko alag alag integrate krlo right side wala to straight up {cotx} aur left side wala {secx} aur {-cosx} ban jayega ab bas jo bracket me hai unhe integrate krlo ans ln|secx+tanx| -sinx+log|sinx| aajaega.
This question answer is log|secQ +tanQ| -sinQ +log|sinQ|+c
Bhai integration se hard toh A.P G.P aur Binomial ke questn aate hai😂💀
Bhai kahi tum PNC aur probability ko bhul to nhi gaya h😅
@@ram.......111 sab hi hard
Relatable 😅 me bhi ques. puchne gaya tha.
question me dQ nahi lgaya hai
btw i am in 10th class but i like calculus
Bhaiya correction window me category change ka option nhi aa rha h
But still they have time for uploading videos😂😂
Ans: ln|secx+tanx|-sinx-ln|cosecx|+C
This is the simplest question of integration...
If u do integration by parts that is the easiest question
Itna aasan question hai mind mein hi solve hi gaya waise
Separate krke solve kro phir tan ko sin ke form cosec ko bhi usi form mein likhe substitute krdo
Bhaiya ek question tha..
Maine 11th and 12th me jee ka kuch bhi nhi padha but mujhe ab jee krna hi hai please aap batao ki kya kru . Mai bohot chote Village se hu mujhe koi bhi guide krne wala nhi hai
Mai Neet wali hun par mere se to solve ho gaya😂 kyunki I am PCMB student😅
Neet student hoke ye question solve karne ka ghamand hai😎😎
Same here 😅
Aur hame Jee student hoke na karne ka ghammand h😂😂😂😂
Iska ghamand hai
Lekin chaar saal drop lene ka ghamand nhi hai
Maha easy question hai
10th mai solve karne ka ghamand hai😂😂
Correct answer is sec thetta.class 10 th walo like karo.
Hahaha
Bhaiya cengage ka Nasha kar rahe 😂😂
Bo nerves physical body me nahi hoti he aur bo nadi hoti hai ida , pingla and susuma
To integrate the given expression, we can start by rewriting it in a more tractable form:
sin(theta)tan(theta) + cosec(theta)cos(theta)
= sin(theta)(sin(theta)/cos(theta)) + (1/sin(theta))(cos(theta))
= (sin^2(theta) + cos(theta))/cos(theta)
= (1 + cos(theta))/cos(theta) (using the Pythagorean identity sin^2(theta) + cos^2(theta) = 1)
= sec(theta) + 1
Now, we can integrate:
∫(sec(theta) + 1) dtheta
= ∫(1/cos(theta)) dtheta + ∫(1) dtheta
= ln|sec(theta) + tan(theta)| + theta + C
where C is the constant of integration.
Therefore, the integral of sin(theta)tan(theta) + cosec(theta)cos(theta) is ln|sec(theta) + tan(theta)| + theta + C.
d theta is not given in question how did the whole comment section integerate it anyways?
For sinx tanx = break in sin cos, 1-cos sqaure/ sin , take sin t and alag alg solve khatam
Now the next funtion break in sin cos, sin se multiply upr niche, 2sixcos=dt and sin sqaure x=t
Khatam
Bhai second function ke liye sirf sinx=t lelenge fir upar toh cos Hae hi
Bro he can't do the first question💀💀
Bhai ye question mera math ke exam me aya tha iss baar 10 me CBSE 😂😂😅
Me just after 10th learning integration for the first time and trying to solve with basic knowledge😂😂
Same here jab bhi me ghar aata hu mera bhai mere liye questions ki poori book banake rakhta hai😢😢❤❤
Assan to hai bhai 💀 ye to ncert mei puchte hai
Lekin ek minute...
Chota bhai 12th mein hai isiliye integration ke questions solve kar raha aur bada bhai do saal se IIT ki taiyari kar raha hai matlab woh drop year mein hai, yeh kaise sambhav hai.
Answer is log(tanx+secx)-sinx+log(sinx)
Oh wow i remember solving this same integration as a step for a countour integration. Pyare jee ke daya the
Bhai thode Capital “C” ho kya ?? Pls reply
Mai medical ka student hu par meri trigonometry 10th me best thi.
Iska answer tan@sin@ +cot@ hai, ya ise seedha sin²@/cos@+cos@/sin@
bro be sniffin em maths problems 💀
Bro you chose the wrong comment section people here won't understand the humour 😭
@@neerubalamakeover9097 i didn't commented for the sake of attention, i genuinely felt too do so, and your point is true as well
best thing to do is multiply both side by 0 , proved
its not proving kiddo its about finding the value !!
The correct answer to this question is ln(tanx+secx)+ln(sinx)-sinx+C we are taking theta is equal to x here since I don't know how to write theta in keyboard
Motion Learning Aap Hai Na Sbhi Problem ha Solution '♥✨
Use by part
Best method to solve integration is remember 15. Ways or type of inte. Method which ur good teacher gave u in notes
Aur xam m 1 min phir last m inte ka ques ko time deena
Jisne video banaya usse kuch nahi malum. Theta and x are both arbitrary variable. So substitution should be different
Wo jee ki nhi neet ki tayari kar rha hoga dekho 😂😂😂
Solution:
1.Write the expression in terms of sinx and cosx.
2.Convert all sinx into cosx using [(sinx)^2 +(cosx)^2 =1]
3.Divide and break the fraction (a-b/c =a/c-b/c)
Remaining: secx-cosx+cosecx.cotx
Now integrate...
Answer: ln(|secx+tanx|) - sinx - cosecx + c
Wo sab htao bhai ques me d theeta to hai hi nhi 😂😂 integerate kiske respect me kre
😂😂😂😂
Common sense h bhai d theta sei krega aur kisse krega
@@dakshmehta4498 hm wo hai but mathematically to ques glt hi hua na 😂
D theta valuable hai broo
@@dakshmehta4498exam me common sence nhi chalta marks katte he
Ans
ln|sec× + tan×| - sin× + ln|sin×| + C
From chat gpt
To solve the expression \(\sin\theta \tan\theta + \csc\theta \cos\theta\), let's break it down into simpler parts using trigonometric identities.
1. \(\tan\theta = \frac{\sin\theta}{\cos\theta}\)
2. \(\csc\theta = \frac{1}{\sin\theta}\)
Using these identities, the expression becomes:
\[
\sin\theta \left(\frac{\sin\theta}{\cos\theta}
ight) + \left(\frac{1}{\sin\theta}
ight) \cos\theta
\]
Simplify each term separately:
\[
\frac{\sin^2\theta}{\cos\theta} + \frac{\cos\theta}{\sin\theta}
\]
Combine the fractions over a common denominator:
\[
\frac{\sin^2\theta \sin\theta + \cos^2\theta \cos\theta}{\cos\theta \sin\theta}
\]
Simplify the numerator:
\[
\frac{\sin^3\theta + \cos^3\theta}{\cos\theta \sin\theta}
\]
Since the numerator cannot be simplified further with common trigonometric identities, the expression \(\sin\theta \tan\theta + \csc\theta \cos\theta\) simplifies to:
\[
\frac{\sin^3\theta + \cos^3\theta}{\cos\theta \sin\theta}
\]
Therefore, the simplified form of the given expression is:
\[
\frac{\sin^3\theta + \cos^3\theta}{\cos\theta \sin\theta}
\]
The answer to that question is
ln | tanx + sinx tanx | -- sinx + C
Put theta instead of x
Ans - ln(secx + tanx) - sinx + ln(sinx)
That badminton is my favorite badminton ❤❤😂
Video =🙂
Song=☠️
Answer is:- ln | sec theta ( 1 + cosec theta ) | - sin theta + C
C IS CONSTANT OF INTEGRATION OR YOU CAN SAY
YOU ARE THAT “C”
Bro d theta is not given
Aare yaar "dx" hi toh nahi hai, integration kaise hoga ...🎃🎃( x ke jagay theta)😅😐🥴🎃
Last me *dx* nahi hai question wrong
This Integral is not valid as there is no 'dθ' hence no solution.
Jo question tune dikhaya hai us question ka ans ek line nikalata hu main😂😂😂
Itna easy to hai bs add per break krke multiplication rule lgana h
Sin and cos main convert krke sin²x ko 1- cos²x likhee separate...simpleee😄💯