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Question

If (α+β)=π2 and (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
α+β=π2α=π2βtanα=cotβ

tanαtanβ=1
Next, β+γ=α
αβ=γtanαtanβ1+tanαtanβ=tanγ
tanαtanβ=2tanγ
tanα=tanβ+2tanγ.

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