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Question

If α+β=π2and β+γ=α then tanα equals

A
2(tanβ+tanγ)
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B
tanβ+tanγ
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C
tanβ+2tanγ
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D
2tanβ+tanγ
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Solution

The correct option is C tanβ+2tanγ
Given tan(α+β)=π2tanα.tanβ=1.........(i)
Also α=β+γtanα=tanβ+tanγ1tanβ.tanγ
tanα=tanβ+tanγtanαtanγtanα using.........(i)
tanα=tanβ+2tanγ

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