If 3 = 4 (x + ) (x - ), then x = - Vidyadip

MCQ

If $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha ),$ then $x = $

A
$n\pi \pm \frac{\pi }{6}$
✓
$n\pi \pm \frac{\pi }{3}$
C
$n\pi \pm \frac{\pi }{4}$
D
$n\pi \pm \frac{\pi }{2}$

✓

Answer

Correct option: B.

$n\pi \pm \frac{\pi }{3}$

b
(b) $3\sin \alpha - 4{\sin ^3}\alpha = 4\sin \alpha ({\sin ^2}x - {\sin ^2}\alpha )$

$\therefore $ ${\sin ^2}x = {\left( {\frac{{\sqrt 3 }}{2}} \right)^2}$

==> ${\sin ^2}x = {\sin ^2}\pi /3$

==> $x = n\pi \pm \pi /3$.

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