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Question

If tanβ=2sinαsinγsin(α+γ), then cotα,cotβ,cotγ are in:

A
A.P
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B
G.P
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C
H.P
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D
None of these
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Solution

The correct option is A A.P
tanβ=2sinαsinrsin(α+g) [Given]
tanβ=2sinαsinrsinαcosr+cosαsinr
tanβ=2sinαcosr+cosαsinrsinαsinr=2cotα+cotr
cosα+cotr=αcotβ
cotα,cotβ and cotr are in AP.

1119925_1201884_ans_f57861b688384eaa8db0efd462cb77b4.jpg

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