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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=π2β=π2α
β+γ=αγ=2απ2
tanβ+2tanγ=tan(π2α)+2tan(2απ2)=1tanα21tan2α2tanα=tan2αtanα=tanα

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