00:01
All right, we wish to prove that 1 minus cosine squared theta over 1 plus the sine of theta is equal to the sign of theta.
00:23
And we are going to work on the left side of this proof, try to make it look like the right side.
00:39
That's the way we do it.
00:41
Usually we start with the more complicated side.
00:43
And the first thing i notice here is that on the right, everything, all i have is sign of theta there.
00:48
So i'm going to want to get rid of this cosine squared of theta.
00:51
And the thing that i recognize is we have a pythagorean identity.
00:56
And we should be used to the idea by now that one of the forms of the pythagorean identity, cosine squared equals one minus the sine square of theta.
01:09
So if i make that substitution, i'm going to have one minus, one minus, one minus.
01:16
The sine squared of theta over one plus the sine of theta...