00:01
Prove the equation is an identity.
00:04
Well, i'm going to work on the left -hand side and start with the identities for sign of a sum and then sign of a difference.
00:12
So, sign of the sum is sine a cosine b plus cosine a, sine b.
00:22
So that's, and i'm going to wrap that in parentheses, the sign of a difference is sine a cosine.
00:30
B minus cosine a sine b we can now multiply these two parentheses just like any other binomial and i notice that they are exactly the same except one's a positive one's a negative which means we have a difference of two squares so a difference of two squares says i'm going to have sine a cosine b squared minus cosine a, sine b squared.
01:09
Let's continue this.
01:10
This will be sine squared a, cosine squared b, minus cosine squared a, sine squared a, sine squared a, sine squared b.
01:21
We look and see, we're very close to what we need.
01:25
So i'm going to come over here and say, well, i can't factor anything out, but i need to have just cosine b in this first one, in the second one.
01:36
Looking where i need to go.
01:37
I say i need cosine b in the second one and cosine a in the first one, but we have it backwards.
01:44
And we don't want these signs...