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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 Ctanβ+2tanγ Given tan(α+β)=π2⇒tanα.tanβ=1.........(i) Also α=β+γ⇒tanα=tanβ+tanγ1−tanβ.tanγ ⇒tanα=tanβ+tanγtanα−tanγtanα using.........(i) ∴tanα=tanβ+2tanγ