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Question

Prove that:
sinx+sin3x+sin5x+sin7x=4cosxcos2xsin4x

Solution
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LHS=sinx+sin3x+sin5x+sin7x=sinx+sin7x+sin3x+sin5x
=2sin4xcos3x+2sin4xcosx=2sin4x(cos3x+cosx)
=4sin4xcosxcos2x
=RHS

Hence proved

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