доказать тождество: (cosx-cos2y)^2+(sinx-sin2y)^2=4sin^2*(x+2y/2)

Question

доказать тождество: (cosx-cos2y)^2+(sinx-sin2y)^2=4sin^2*(x+2y/2)

Answer 1

Используемые формулы

Cos x - Cos y = -2(Sin(x + y)/2)*(Sin(x-y)/2)

Sin x - Sin y = 2(Sin(x-y)/2)*(Cos(x+y)/2)

(Sin x)^2 + (Cos x)^2 = 1

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