00:01
For this problem, we're going to verify this identity that we see above.
00:05
Some of these identities can be quite complicated.
00:08
We typically try to pick the more convoluted looking side and try to simplify it.
00:14
But when we look at this identity, both sides look just about as complicated as the other.
00:20
However, the sine alpha plus beta is special.
00:24
And the sine alpha plus beta, we see that an identity here can be applied.
00:30
So that's a good suggestion for this one to start with the left -hand side, which is sine alpha plus beta, divide by sine alpha times cosine beta, and we'll begin simplifying through this trigometric identity until we hopefully reach the right -hand side, 1 plus cotangent alpha times tangent beta.
00:55
So next, i'll leave extra space in the numerator and apply the trig identity for sign.
01:01
It becomes sine alpha times cosine beta plus cosine alpha times sine beta.
01:13
And let's promote this division bar so that it goes all the way...