00:01
We've got a triangle with angles alpha, beta, and gamma.
00:03
Let's prove that the sign of gamma is equal to the sign of alpha plus beta.
00:08
All right, so starting off, let's determine what gamma really is.
00:13
Well, the sum of all angles in a triangle is 180.
00:17
So gamma is going to be 180 minus the measure of angle alpha minus the measure of angle beta.
00:24
Or, more specifically, 180 minus the combined sum of alpha plus beta with those parentheses there.
00:33
So now with any algebra you can do the same action to both sides.
00:38
So let's apply a sign so this looks more like what our goal is.
00:41
That is, we will have sine of gamma is equal to sign of this whole term, 180 minus parentheses alpha plus beta.
00:55
All right.
00:55
Now with this, this looks an awful lot like a certain identity we have.
01:00
Now, we are an identity in the book saying that if you have the sign of two terms x minus y, this is equal to sine of x times cosine of y minus cosine of x times sine of y.
01:21
All right, well let's apply this identity to our equation here.
01:26
In this case, our x term is going to be this 180 and our y term is going to be alpha plus beta...