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Question

If α,β,γ are in A.P. show that cotβ=sinαsinγcosγcosα.

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Solution

We have,

α,β,γ are in A.P.

So,

2β=α+γ ……… (1)

R.H.S

=sinαsinγcosγcosα

=2cos(α+γ2)sin(αγ2)2sin(γ+α2)sin(αγ2)

=cos(α+γ2)sin(α+γ2)

=cotβ

Hence, proved.


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