If α+β=2πand β+γ=α then tanα equals

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

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Question

If $α + β = \frac{π}{2}$ and $β + γ = α$ then $tan α$ equals

2 (tan β + tan γ)

tan β + tan γ

tan β + 2 tan γ

2 tan β + tan γ

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Evelyn Discussed

α + β = \frac{π}{2}

and

β + γ = α

then

tan α

equals

6 mins ago

Discuss this question LIVE

6 mins ago

Given

tan (α + β) = \frac{π}{2} \Rightarrow tan α . tan β = 1

.........(i)
Also

α = β + γ \Rightarrow tan α = \frac{tan β + tan γ}{1 - tan β . tan γ}

\Rightarrow tan α = \frac{tan β + tan γ}{tan α - tan γ} tan α

using.........(i)

∴ tan α = tan β + 2 tan γ

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Question Text	If $α + β = \frac{π}{2}$ and $β + γ = α$ then $tan α$ equals
Answer Type	Text solution:1
Upvotes	150