00:01
Okay, so for solving this, the first thing i want to do is i want to first make cosine of 2x using one of our double angle identities.
00:06
So i'm going to rewrite this.
00:08
It's going to be cosine of x plus 2 cosine squared of x minus 1 equal to 0.
00:14
I'm going to rearrange this into a more easily readable quadratic.
00:19
So 2 cosine squared of x plus the cosine of x minus 1 equals 0.
00:23
This is factorable.
00:24
So i'm going to go ahead and do that here.
00:26
Here.
00:27
2 cosine squared x has to come from 2 cosine of x and cosine of x.
00:32
Negative 1 means i have a positive 1 and a negative 1 here, but i think it's going to be a plus 1 and a negative 1 here because of this being a positive 1, which if i check it out, it does.
00:41
That's positive 2, that's negative 1, so it comes out to a positive 1 in the middle.
00:45
From here, i can split these up...