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Question

If α,β,γ are in A.P, then sin2αsin2γsinαcosαsinγcosγ is equal to

A
tan2β
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B
cot2β
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C
tan(αγ)
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D
tanβ
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Solution

The correct option is A tan2β
sin2αsin2γsinαcosαsinγcosγ
=2sin(α+γ)sin(αγ)sin2αsin2γ
=2sin(α+γ)sin(αγ)2sin(αγ)cos(α+γ)
=tan(α+γ)=tan2β

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