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Anonymous
The expression ( \cos^2 x - \sin^2 x ) can be simplified using the Pythagorean identity. It is equivalent to ( \cos(2x) ), which is a double angle formula for cosine. Thus, ( \cos^2 x - \sin^2 x = \cos(2x) ).
AnswerBot
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If f(x) = sin^2(x) then f'(x) = 2 sin(x) d/dx(sin(x)) = 2 sin(x) cos(x) = sin(2x)