Why does sine squared plus cosine squared equal 1?

Have you ever been told that sine squared plus cosine squared equals one? Did your teacher explain why that's true? This is the most important pythagorean identity in all of trig (trigonometry), and it's never explained! In this video we'll show why sine squared plus cosine squared must equal one!

[@RexEnrico]

So obvious! After you explained it, thank you ;)

[@goddess_ofchaos]

I'm in my 3rd year of astrophysics and never stopped to ponder about this until I became a maths tutor and explained this rule to a student who had never heard of this, it was hard to explain not knowing why this is true myself so I had to tell her I'd get back on this subject next lesson. Maths just never dissapoints.

[@benchelnitsky]

Great simple proof

[@gurkirarsaluja8227]

Haths of you sir. What a proving tequnique you have.
It Helps me a lot.

[@weiyan7064]

Thank you so much for providing a different way of seeing this question! It saves my life of explaining it to my students!

[@shubhamsrivastav405]

these video is very helpful

[@maxgibson5131]

Probably the clearest explanation I've ever gotten from a math youtube video

[@sumansaxena2418]

Wow!!!! This is so easy!!! Thank you very much for giving such a nice explanation. You have helped me a lot with my exam!!! Thanks a lot and amazing video 👌🏻👌🏻👌🏻👌🏻👌👌👌👌❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍

[@anron5754]

best explanation! Thank you so much!!!

[@astranautic]

This was a super helpful video! I always have trouble getting problems right if I don’t understand exactly why the answer is the right one. And I was even able to figure out the one you provided at the end of the video! With quarantine right now I’m struggling with school and so I felt proud of myself for getting this one. Thank you so much!

[@SumanSingh-eb7qo]

You write too much here boring to read 😒 ;
Bulshit

[@pooltablemechanic]

@@SumanSingh-eb7qo Pendejo!

[@user-sw1zw1uz8i]

Thank you. Really helped me a lot.

[@Joe-uz7qm]

Could you tell me, whether the following proof is correct or not :)?
Consider:
1. tan(x) := sin(x)/cos(x),
2. sin²(x) + cos²(x) = 1 (as you've proven in this video),
3. sec(x) := 1/cos(x).
Hence:
1 + tan²(x) = cos²(x)/cos²(x) + sin²(x)/cos²(x) = (cos²(x) + sin²(x))/cos²(x) = (sin²(x) + cos²(x))/cos²(x) = 1/cos²(x) =: sec²(x). □

[@catcat-jx2bz]

BRILLIANT!

[@niceguy4801]

Thankyou sir!

[@novagirl3219]

Thank you for explaining this...😃

[@rajilakshimi1829]

Really it's useful.. 🙏

[@zerere_]

WOW IT'S SO EASY PROOFS ARE THE COOLEST THANK YOU

[@gordonwang9667]

i've wasted like 20 mins on the internet searching for something like this. Thank you for explaining this clearly to me

[@mjtv2188]

Always wondered why thanks for the answer

[@drewmuantee2836]

Thnks so much

[@antonioprgomet5168]

Amazing video❤️

[@elqaqshorts6877]

thanks

[@meriemladjal1613]

OOOOOO thank you sir i'm from Algeria and i've undrestand verry well thank you sir

[@shadowbane7401]

Can you make a video about why a^(-1b)=1/a^b

[@SimpleMath]

Check out my video about negative powers: ruclips.net/video/QH-QZDJctpw/видео.html

[@rush9727]

sir can't we prove this by cos2x formula

[@vinithaprem2583]

Thank u so much sir..helped me a lot..

[@ranbirsingh-rh7hh]

So what's the role of angle theta
And what is difference between sin and its angle

[@urmom-tu7le]

thank you so much, random internet man. you ended my torment

[@sciencegeek2791]

Why dont we write them as (sinx)^2+(cosx)^2=1 please explain

[@BobBob-uv9fq]

Very good ,really good brief video ,,,very clear

[@MurunGD]

Thx. Subbed

[@vohidovshoxrux-cr3gc]

Zur gap yuq

[@arshadhusain7541]

Grt solving..... Ty

[@davinho8464]

Thanks dawg!

[@nolanbrewer6459]

is there any way to derive this identity if sin^2x+cos^2x have coeficients? for ex what would asin^2x + bcos^2x equal?

[@sparemedat5453]

If you mean derivatives it’s
2acos^2x - 2bsin^2x

[@asustai413]

Theta is missing in the thumbnail!

[@ian9068]

Brilliant and perfect video

[@afnanadit1029]

Nice man

[@guduhandique6792]

Why a^2+b^2=c^2??

[@akashrao3272]

helpline

[@pranav.itis45321]

Pythagoras thearom

[@bjorneriksson6480]

If you learn the unit circle, imprint it in your minds eye, the answer is obvious, no calculation needed, you see it instantly.

[@omchouhan6132]

Bro where is thetha with sin and cos

[@forcircket1537]

cos(α)2+cos(β)2+cos(γ)2=1,
Proof this

[@josh_kem3412]

tysm

[@kirlmboss6352]

OH MAN, only 2 month left before exam to get into university. WISH ME LUCK

[@lozio2352]

I don't understand why it's not (a^2 +b^2) / 2c^2? Why don't you add the two c's?

[@AshmitManak]

We took LCM.

[@lozio2352]

I thought maybe you were being sarcastic but then i looked it up. Thanks Ashmit! 👍For some reason i doing it when numbers were the denominator but not variables, doh!

[@AshmitManak]

Welcome, Lo. Btw in which country you live. As in mine one, we study this in 10th grade.

[@lozio2352]

@@AshmitManak I'm sure we do too here in the UK but I've come to math late in life. Back in my school days i had other dramas going on...

[@soerenna]

thanks a lot man:)

[@hml3672]

A*2/c*2 is not = (a/c)*2

[@anmolsingh6158]

Thy

[@lulitacaicedo]

thanks :)

[@anowarmahabub2296]

i love u

[@RammusTheArmordillo]

Lol I graduated and I don't know what sec(x) is

[@vanste9876]

I think that they call sec arc-thing....like arcsin or arccosin...not really sure

[@archer5922]

Stevan Okulic with arc sin being the inverse of sin and same for cos

[@enamoloper3742]

He just took theta as x, don't worry.

[@Math-xb1ml]

i ask teacher why he didn't respond thank you 😇
i hope my teachers answer my hows

[@goodnic3]

arigato go​ sai mus

[@graysonconnel5439]

i love you

[@aatrox5559]

ow cool

[@nataliehanks3308]

BRUH.

[@Jessica-hl4mo]

good soup

[@study-my4hk]

I went aaaaaah wwwOOOW.

[@DDG00]

Cawk is hot

[@aayushmishra7727]

BINOD

[@HakanAkar710]

So obvious! After you explained it, thank you ;)