If + = 2 and + = , then , equals - Vidyadip

MCQ

If $\alpha + \beta = \frac{\pi }{2}$ and $\beta + \gamma = \alpha ,$ then $\tan \,\alpha $ equals

A
$2\,(\tan \beta + \tan \gamma )$
B
$\tan \beta + \tan \gamma $
✓
$\tan \beta + 2\,\tan \gamma $
D
$2\,\tan \beta + \tan \gamma $

✓

Answer

Correct option: C.

$\tan \beta + 2\,\tan \gamma $

c
(c)$\alpha + \beta = \frac{\pi }{2} \Rightarrow \tan \beta = \cot \alpha $
$\tan (\beta + \gamma ) = \tan \alpha $ ==> $\tan \alpha = \frac{{\tan \beta + \tan \gamma }}{{1 - \tan \beta \tan \gamma }}$
==> $\tan \alpha = \frac{{\cot \alpha + \tan \gamma }}{{1 - \cot \alpha \tan \gamma }}$
==> $\tan \alpha - \tan \gamma = \cot \alpha + \tan \gamma $
==> $\tan \alpha = \tan \beta + 2\tan \gamma $.

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