Thank you sir, I am a passionate mathematics lover, I love and aim to understand every mathematical concepts at deeper level, I appreciate your explanation sir
Thank you so much sir for giving us the intuition behind this formula, otherwise in most of the schools or coaching they just directly give the formula to mug it up with zero conceptual clarity.
When (a+b) is obtuse, we are entering into the territory of sin(x) being a real function rather than just being a trigonometric ratio. So we will use the unit circle rather than using a right angle triangle. For proving the compound angle identity for obtuse angle, refer to the proof of cos(A+B) from below link, then write sin(A+B) = cos(90-(A+B))=cos((90-A)-B)=cos((90-A)+(-B))=cos(90-A)cos(-B) - sin(90-A)sin(-B) and you will get the desired result. You can also refer to above method in NCERT of Class XI, page number 59, chapter 3. ruclips.net/video/NTIb-bQ2It4/видео.html
@@shivam-kharkhate Yes, another way of proof is given in SL loney too. All these methods are more or less same, using the concepts of allied angles in one way or another. And if you refer to section 92 of SL Loney book, the term "Trigonometric Functions" is used instead of trigonometric ratios, when referring to the proofs.
@@shivam-kharkhate Yes, this method will work but we will have to go in the territory of trigonometric functions. For example, in the proof shown in this video, the length which is shown as sin(A+B) is very much clear from the diagram using the right angled triangle. But lets say when (A+B) is obtuse or lies in 3rd or 4th quadrant, the length will still be taken as sin(A+B) with appropriate signs. When we go beyond 90 degrees, we no longer talk about trigonometric ratios, we talk about trigonometric functions. We take the x and y coordinates of unit circle as (cos(theta), sin(theta)). The length taken as sin(A+B) in this diagram, will actually come from the y coordinate of the point when (A+B) is obtuse. As mentioned in SL Loney- "The same proof will be found to apply to angles of any size, due attention being paid to the signs of quantities involved". It means when (A+B) is lying in 3rd quadrant, the y coordinate will still be sin(A+B) but it will be a negative quantity. If we want to use it as a length, we will have to use a negative sign.
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Easiest proof of sin(A+B) and cos(A+B) formula in one shot
ruclips.net/video/lco1bPYkBSc/видео.html
Thank you sir, I am a passionate mathematics lover, I love and aim to understand every mathematical concepts at deeper level, I appreciate your explanation sir
Glad you liked it !!
Thank you so much sir for giving us the intuition behind this formula, otherwise in most of the schools or coaching they just directly give the formula to mug it up with zero conceptual clarity.
I'm BIOS student but I love maths formulas derivations I love in knowing from where these formula came from.
You did great job.👍🙏
Hey our thinking does match then!!
Thanks a lot sir. I was struggling with this for hours.
Wonderful. From Pakistan 🇵🇰
Beautiful . Indie teacher salute !
Thank you !!
Great job, Sir. Simple and intuitive
Thts the best explanation i have seen so far
Proof when (a+b) obtuse angle
When (a+b) is obtuse, we are entering into the territory of sin(x) being a real function rather than just being a trigonometric ratio. So we will use the unit circle rather than using a right angle triangle.
For proving the compound angle identity for obtuse angle, refer to the proof of cos(A+B) from below link, then write sin(A+B) = cos(90-(A+B))=cos((90-A)-B)=cos((90-A)+(-B))=cos(90-A)cos(-B) - sin(90-A)sin(-B) and you will get the desired result.
You can also refer to above method in NCERT of Class XI, page number 59, chapter 3.
ruclips.net/video/NTIb-bQ2It4/видео.html
@@niteshjakhar sir according to s.l loney book --- the same proof will be found to apply to angles of any size
@@shivam-kharkhate Yes, another way of proof is given in SL loney too. All these methods are more or less same, using the concepts of allied angles in one way or another.
And if you refer to section 92 of SL Loney book, the term "Trigonometric Functions" is used instead of trigonometric ratios, when referring to the proofs.
Will This method of proving work when a, b of any size.
@@shivam-kharkhate Yes, this method will work but we will have to go in the territory of trigonometric functions. For example, in the proof shown in this video, the length which is shown as sin(A+B) is very much clear from the diagram using the right angled triangle. But lets say when (A+B) is obtuse or lies in 3rd or 4th quadrant, the length will still be taken as sin(A+B) with appropriate signs. When we go beyond 90 degrees, we no longer talk about trigonometric ratios, we talk about trigonometric functions. We take the x and y coordinates of unit circle as (cos(theta), sin(theta)). The length taken as sin(A+B) in this diagram, will actually come from the y coordinate of the point when (A+B) is obtuse.
As mentioned in SL Loney- "The same proof will be found to apply to angles of any size, due attention being paid to the signs of quantities involved". It means when (A+B) is lying in 3rd quadrant, the y coordinate will still be sin(A+B) but it will be a negative quantity. If we want to use it as a length, we will have to use a negative sign.
Will the formula work if A+B>90?
yes the formula is always applicable
@@niteshjakhar thank you
No
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The background is simply power point and my image is on the front. That's it.
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