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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 D tanβ+2tanγ
Given,
α=(π2β) and γ=αβ

α and β are complementary

tanα=cotβtanαtanβ=1

tanγ=tanαtanβ1+1tanα=tanβ+2tanγ

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