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1 Answer
- 1 decade agoFavorite Answer
cos(2x) = cos(x+x)
by the formula for cosine of sum of two angles, which you probably have already learned,
cos(x+x) = cos(x)cos(x) - sin(x)sin(x) = cos^2(x) - sin^2(x)
also, because cos^2(x) + sin^2(x) = 1 by the pythagorean identity, cos(2x) = 1-sin^2(x) - sin^2(x) = 1-2sin^2(x)
by similar reasonining, cos(2x) = 2cos^2(x) - 1
so cos(2x) = cos^2(x) -sin^2(x) = 2cos^2(x) - 1 = 1 - 2sin^2(x)