# Trig manipulation troubles

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...

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What about just cos2x = 1 - sin2x?

Evil, evil trig...
Certainly hear you:)

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

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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)