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Prove that cos2x = {(cos^2x - sin^2x), (2cos^2x - 1), (1 - 2sin^2x), ((1 - tan^2x)/(1 + tan^2x))

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Prove that cos2x = {(cos2x - sin2x), (2cos2x - 1), (1 - 2sin2x), ((1 - tan2x)/(1 + tan2x))

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We have cos(x + y) = cos xcos y – sin xsin y 

Replacing y by x, we get 

cos(x + x) = cosx cosx-sinx sinx

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