Compound Angle Identities (1 of 3: Proving sin(a+b) geometrically)

[PrakashkumarS]

I regret not having a math teacher who can teach like you do. Good job Eddie

[v._.v]

it's funny since our teacher couldn't teach for some reason, then he just link ur videos for us to self-learn XD

[ActuallyAudacity]

Thanks for this video. I missed a day on my Year 13 Maths lesson and was utterly clueless. This video saved me no lie.

[oscarlima]

The ancients of the past tried many times and found this " crazy" very logical structure to proove it. There are other ways to prove it, but they require more advanced mathematics...

[NickEnchev]

This is one of those videos that has such a good visual representation and explanation of the idea its trying to convey that I instantly had an "aha!" moment.

[mrsunto]

Omg, at the end I literally felt so happy that I started smiling, it felt such a big achievement. Lol😆😽

[schenzur]

I got the proof but the only question that I have is that crazy structure. How do you come up with it, I mean that structure seems random, I want to know the thought process of making that structure. If you can make a vid about it, it would be great.

[endaodonnell]

that explanation was amazing, made my life easier

[shivam-kharkhate]

Proof sin(a+b) in unit circle taking (a+b) greater than 90 degree

[AshleyTyagi]

At 5:36 on that triangle with cosb and sinb doesnt that prove sin^a + cos^a = 1 ?

[Kindiakan]

I proved this identity by considering the area of a triangle with the contained angle a+b. Splitting that triangle into two triangles with contained angles a and b respectively, then equating the sum of the areas of those triangles with the area of the triangle that they make up. Simplification gets me the result as desired.

[doctorarms]

what side of the triangle would cos(a+b) be then?

[hemaroy]

It is quite easy to solve with unit circle!

[alexdias]

In what year of school do u have to learn this?

[gregorywade]

What software is he using with his stylus? Works better than mine.

[jyothieswar]

why OP length should be equal to 1
only doubt i had in this video
i hope u clear this soon sir

[sarehbagherichimeh]

if its in a unit circle isn't cos(beta) just 1? why can't we consider it 1?

[manasraj]

At 0:45, how is that thing an identity?

[u]

I'm sorry, but this presentation falls short of proving the identity. The geometry of the diagram serves only to show that the relation holds for two positive angles that are each less than 90 degrees. There is no justification in the presentation as to why the relation holds for ALL pairs of angles (which, in fact, it does). To make such a claim without justification does nothing to instil a sense of reasoning into students' minds. Example: If I take the number 10 (an even number) and divide it by 2, I get 5 (an odd number). So, it must always be true that dividing any even number by 2 results in an odd number. This is patently nonsense, but I've used the same bogus logic as is used in this presentation. This clunky old proof is the same one my maths teacher trotted out 50 years ago. We did go on to show that the relation was, in fact true for all angles, but that required rather more work. But, why use this proof at all when there is a much more elegant proof available that uses simple co-ordinate geometry and doesn't suffer from the glaring shortcomings of the proof presented here, which should have been put out of it's misery years ago.

[WahranRai]

Another way to prove it by using Euler formula (complex number) : exp(i*A) = cosA + i*sinA --->
exp(i*(A+B)) = exp(i*A)*exp(i*B) = (cosA + i*sinA)(cosB + i*sinB) = cosA*cosB + cosA*i*sinB + i*sinA *cosB +i*sinA *i*sinB
exp(i*(A+B)) = cos(A+B) + i*sin(A+B) = cosA*cosB - sinA*sinB + i*(cosA*sinB + sinA *cosB ) --->
By equalizing the real and imaginary parts : cos(A+B) = cosA*cosB - sinA*sinB and sin(A+B) = cosA*sinB + sinA *cosB