Trig identities for $A\sin^2(x)+\cos^2(x)$

Does anyone know of any useful trig identities for manipulating $A\sin^2(x)+\cos^2(x)$? The only thing I come up with is:

$A\sin^2(x)+\cos^2(x)=\frac{1}{2}(1+A)+\frac{1}{2}(1-A)\cos(2x)$

I'm trying to manipulate it to see if a more complex expression including this sub-expression will simplify any, so that it is integrable.

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$1 + (A-1)\sin^2(x)$ :) –  Lagerbaer May 5 '11 at 20:18
What you've come up with is already pretty easy to integrate. For the purposes of integrating, I don't really think you can do better. If you're having trouble with the more complex expression you might just want to post the whole thing. –  Qiaochu Yuan May 5 '11 at 20:33
@Qiaochu Yuan: I've posted the actual integral in another question here. –  okj May 5 '11 at 22:32