If = 1 7 , ; = 1 3 , then 2 = - Vidyadip

MCQ

If $\tan \alpha = \frac{1}{7},\;\tan \beta = \frac{1}{3},$ then $\cos 2\alpha = $

A
$\sin 2\beta $
✓
$\sin 4\beta $
C
$\sin 3\beta $
D
None of these

✓

Answer

Correct option: B.

$\sin 4\beta $

b
(b) $\cos 2\alpha = \frac{{1 - {t^2}}}{{1 + {t^2}}} = \frac{{24}}{{25}}$ {Here $t = \tan \alpha $}

$\sin 2\beta = \frac{{2T}}{{1 + {T^2}}} = \frac{3}{5} \Rightarrow \cos 2\beta = \frac{4}{5}$ {$T = \tan \beta $}

$\therefore \,\,\sin 4\beta = 2\sin 2\beta \cos 2\beta $

$= 2.\frac{3}{5}.\frac{4}{5} = \frac{{24}}{{25}} = \cos 2\alpha $.

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