If α+β=π2 and β+α=α, then tan α&#

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Question

If

α + β = \frac{π}{2}

and

β + α = α

, then

t a n α e q u a l s

Options:

A . 2(tan β+tan γ)

B . tan β+tan γ

C . tan β+2tan γ

D . 2tan β+tan γ

Answer: Option C
:
C
(c)

α + β = \frac{π}{2} => t a n β = c o t α

t a n (β + γ) = t a n α => t a n α = \frac{t a n β + t a n γ}{1 - t a n β t a n γ}

=> t a n α = \frac{c o t α + t a n γ}{1 - c o t α t a n γ}

=> t a n α - t a n γ = c o t α + t a n γ

=> t a n α = t a n β + 2 t a n γ

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