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Question

sin8αcosαsin6αcos3αcos2αcosαsin3αsin4α=

A
cot2α
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B
tan2α
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C
cos2α
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D
sin2α
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Solution

The correct option is D tan2α
sin8αcosαsin6αcos3αcos2αcosαsin3αsin4α

=2sin8αcosα2sin6αcos3α2cos2αcosα2sin3αsin4α

=sin9α+sin7αsin9αsin3αcos3α+cosαcosα+cos7α

=sin7αsin3αcos3α+cos7α

=2cos5αsin2α2cos5αcos2α=tan2α

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