00:02
All right, to verify an identity, you're going to make changes to the left side of the equation or changes to the right side of the equation or changes to both in order to get to the point where they look identical.
00:13
And you can't bring things from one side of the equal sign to another, so i'm just going to draw a line and we're not going to cross that line.
00:21
And for this problem, we're going to incorporate the pythagorean identity, which says that sine squared alpha plus cosine squared alpha is equal to one.
00:31
Now if i took that and i subtracted cosine squared alpha from both sides, i would have sine squared alpha equals 1 minus cosine squared alpha.
00:41
Or if i went back to the original and i subtracted sine squared alpha from both sides, i would have cosine squared alpha equals 1 minus sine squared alpha.
00:51
So these are both true and we can use them for substitutions.
00:54
So we'll keep that in mind.
00:56
Okay, back to the identity that we're trying to verify.
00:59
So on the left side, i'm going to factor sine squared alpha.
01:02
Out of both terms.
01:03
So that would give us sine squared alpha times one minus sine squared alpha.
01:10
And notice that we've just seen how we can replace 1 minus sine squared alpha with cosine squared alpha.
01:17
So i'm going to rewrite the left side as sine squared alpha times cosine squared alpha...