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Question

Prove that :
(sin7x+sin5x)+(sin9x+sin3x)(cos7x+cos5x)+(cos9x+cos3x)=tan6x

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Solution

LHS=(sin7x+sin5x)+(sin9x+sin3x)(cos7x+cos5x)+(cos9x+cos3x)
=2sin6xcosx+2sin6xcos3x2cos6xcosx+2cos6xcos3x

=2sin6x(cosx+cos3x)2cos6x(cosx+cos3x)

=tan6x=RHS

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