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Question

Prove that: cos3 x sin 3x+sin3 x cos 3x=34 sin 4x

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Solution

We know,cos3x=4cos3x-3cosxcos3x=cos3x+3cosx4 ...iAlso,sin3x=3sinx-4sin3xsin3x=3sinx-sin3x4 ...ii
Now,LHS=cos3x sin3x+sin3x cos3x =cos3x+3cosx4sin3x+3sinx-sin3x4cos3x Using i and ii =143sin3x cosx+sinx cos3x+cos3x sin3x-sin3x cos3x =143sin3x+x+0 =34sin4x =RHSHence proved.

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