How Do You Solve Trig Identity Manipulations?

[Andrusko]

I'm following through a solution to a problem I couldn't do and there's a bit of trig manipulation I can't get my head around:

2cos^{2}x - sin^{2}x = 2 - 3sin^{2}x

I tried using this identity to get it to work:

cos^{2}x - sin^{2}x = 1 - 2sin^{2}x

but alas, I could not. And after that I have no more ideas.

If someone could point out how this transforms that'd be great. Evil, evil trig...

 

[Tedjn]

What about just cos²x = 1 - sin²x?

 

[klondike]

Evil, evil trig...

Certainly hear you:)

How about cos²x =0.5(1+cos2x) and sin²x =0.5(1-cos2x)

 

[The_ArtofScience]

I'm following through a solution to a problem I couldn't do and there's a bit of trig manipulation I can't get my head around:

2cos^{2}x - sin^{2}x = 2 - 3sin^{2}x

I tried using this identity to get it to work:

cos^{2}x - sin^{2}x = 1 - 2sin^{2}x

but alas, I could not. And after that I have no more ideas.

If someone could point out how this transforms that'd be great. Evil, evil trig...

Doesn't that work though?

2(1-sin^2(x)) - sin^2(x) = 2 -2 sin^2(x) - sin^2(x) = 2 - 3sin^2(x)