But even if you just have cos^2(x) or sin^2(x) alone, that identity comes in handy. Here's how.

cos(2x) = cos^2(x) - sin^2(x)
1 = cos^2(x) + sin^2(x)

1 + cos(2x) = 2 cos^2(x)
1 - cos(2x) = 2 sin^2(x)

So sin^2(x) = (1/2)(1 - cos(2x)) and
cos^2(x) = (1/2)(1 + cos(2x))

Those substitutions come in handy and they're very easy to derive if you can't remember them.

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