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Question

if α+β+γ=900, then tan α+tanβ+tanα tanβ cotγ is--.

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Solution

Given:- α+β+γ=90°
To find:- tanα+tanβ+tanαtanβcotγ=?
Solution:-
tanα+tanβ+tanαtanβcotγ
=tan(α+β)(1tanAtanB)+tanαtanβcotγ[tan(A+B)=tana+tanB1tanAtanB]
=tan(90°γ)(1tanαtanβ)+tanαtanβcotγ[α+β+γ=90°]
=cotγ(1tanαtanβ)+tanαtanβcotγ[tan(90°θ)=cotθ]
=cotγcotγtanαtanβ+tanαtanβcotγ
=cotγ
Hence the value of tanα+tanβ+tanαtanβcotγ is cotγ.

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