How can I prove cos^2(5x)-sin^2(5x)=cos(10x)

Prove the identify cos^2 5x - sin^2 5x = cos 10x sin x + cos x^2 = 1 + sin 2x cos^4 x - sin^4 x = cos 2x 2 tan x/1 + tan^2 x = sin 2 x 1 - cos 2x/sin 2x = tan x

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the answer is 48m^2!

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