Which identities did you have in mind? Looks like sin(2x) and cos(2x) might be helpful. Let's see your efforts.
I got to 2 sinx cosx (cos x)= cos^2x-sin^2x but don't know where to go from there. I tried moving everything to one side and setting it equal to zero, then factoring, but that didn't seem to work either. Suggestions?
The advice you've been given is good, and is standard. I'm wondering, though, if anybody else has tried following this through to the end. There are solutions (here), but I'm having a devil of a time arriving at them independently.Here's what I got, but I'm still stuck:
2 sin x(1-sin^2x)=1-sin^2x-sin^2x
2 sin x - 2 sin^3 x=1 - 2 sin^2 x
2 sin^3 x - 2 sin^2 x - 2 sin x +1=0
I can't factor by grouping - I've tried every combination and it doesn't work.
I also thought I might be able to move the 1 to the other side and then factor, but that didn't work either.
2 sin x(sin^2 x - sin x - 1)=-1 but what is left inside the parentheses is not factorable.
Help!
Here's what I got, but I'm still stuck:
2 sin x(1-sin^2x)=1-sin^2x-sin^2x
2 sin x - 2 sin^3 x=1 - 2 sin^2 x
2 sin^3 x - 2 sin^2 x - 2 sin x +1=0
I can't factor by grouping - I've tried every combination and it doesn't work.
I also thought I might be able to move the 1 to the other side and then factor, but that didn't work either.
2 sin x(sin^2 x - sin x - 1)=-1 but what is left inside the parentheses is not factorable.