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Question

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

A
cotβ
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B
tanβ
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C
cotβ
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D
tanβ
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Solution

The correct option is A cotβ
sinαsinγcosγcosα=sinαsinγ(cosαcosγ)=2cos(α+γ2)sin(αγ2)2sin(α+γ2)sin(αγ2)=cot(α+γ2)=cotβ (2β=α+γ)

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