If 2 and , then tan equals [2001]

Question

If $α + β = \frac{π}{2}$ and $β + γ = α$ , then $\tan α$ equals [2001]

Smart Achievers · Accepted Answer

(3)

$Given: α + β = \frac{π}{2} \Rightarrow α = \frac{π}{2} - β$

$\Rightarrow \tan α = \tan (\frac{π}{2} - β) = \cot β = \frac{1}{\tan β}$

$\Rightarrow \tan α \tan β = 1 \Rightarrow 1 + \tan α \tan β = 2$

$Now, \tan (α - β) = \frac{\tan α - \tan β}{1 + \tan α \tan β}$

$\Rightarrow \tan γ = \frac{\tan α - \tan β}{2}$

$\Rightarrow 2 \tan γ = \tan α - \tan β$ $\Rightarrow \tan α = 2 \tan γ + \tan β$

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