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Question

If 0<α,β,γ<π2 such that α+β+γ=π2 and cotα,cotβ,cotγ are in A.P., then the value of cotαcotγ is

A
1
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B
3
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C
cos2β
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D
None of these
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Solution

The correct option is B 3
If cotα,cotβ,cotγ are in A.P., Then
cotα+cotγ=2cotβ=cot(π/2αγ)=2cot(α+γ)(α+β+γ=π/2)

cotα+cotγ=2cotα+cotγcotαcotγ1cotαcotγ=3

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