If ( + ) = 0, then ( + 2 ) = - Vidyadip

MCQ

If $\cot (\alpha + \beta ) = 0,$ then $\sin (\alpha + 2\beta ) = $

✓
$\sin \alpha $
B
$\cos \alpha $
C
$\sin \beta $
D
$\cos 2\beta $

✓

Answer

Correct option: A.

$\sin \alpha $

a
(a) Given, $\cot (\alpha + \beta ) = 0 \Rightarrow \cos (\alpha + \beta ) = 0$

==> $\alpha + \beta = (2n + 1)\frac{\pi }{2},n \in I$

$\therefore$ $\sin (\alpha + 2\beta ) = \sin (2\alpha + 2\beta - \alpha )$

$=\sin {\rm{ }}[(2n + 1){\rm{ }}\pi - \alpha ]$

$ = \sin (\,2n\pi + \pi - \alpha \,)$ = $\sin (\,\pi - \alpha \,)\, = \sin \alpha $.

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