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Question

lf α+β=π2 and β+γ=α, then tanα is equal to

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+β=π2 and β+γ=α

α=π2β

tanα=tan(π2β)=cotβ

tanα=1tanβ

tanα.tanβ=1

1+tanα.tanβ=1+1=2

tan(αβ)=tanαtanβ1+tanα.tanβ

tanγ=tanαtanβ2 [β+γ=αγ=αβ]

2tanγ=tanαtanβ

tanα=2tanγ+tanβ

Hence, the answer is 2tanγ+tanβ.

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