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Question

Prove the following identity:
sinα+sin3α+sin5αcosα+cosα+cos5α=tan3α

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Solution

=sinα+sin3α+sin5αcosα+cos3α+cos5α
=2sin3αcos2α+sin3α2cos3αcos2α+cos3α
=tan3α×(1+2cos2α)(1+2cos2α)
=tan3α

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