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Question

The value of sin8θcosθsin6θcos3θcos2θcosθsin3θsin4θ is

A
cotθ
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B
sec2θ
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C
cot2θ
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D
tan2θ
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Solution

The correct option is D tan2θ
sin8θcosθsin6θcos3θcos2θcosθsin3θsin4θ=2sin8θcosθ2sin6θcos3θ2cos2θcosθ2sin3θsin4θ=sin9θ+sin7θsin9θsin3θcos3θ+cosθcosθ+cos7θ=sin7θsin3θcos3θ+cos7θ=2cos5θsin2θ2cos5θcos2θ=tan2θ

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