calculus

Provide the identity. Show all proper work. 2 sin xcos^3x + 2 sin^3 xcosx = sin(2x)

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  1. 2 sin x ∙ cos³x + 2 sin³x ∙ cosx =

    2 sin x ∙ cos x ∙ cos²x + 2 sin x ∙ cos x ∙ sin² x =

    2 sin x ∙ cos x ∙ ( cos²x + sin² x ) =

    2 sin x ∙ cos x ∙ 1 = 2 sin x ∙ cos x = sin 2x

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