If 2x + 4x = 2 3x, then x = - Vidyadip

MCQ

If $\sin 2x + \sin 4x = 2\sin 3x,$ then $x =$

✓
$\frac{{n\pi }}{3}$
B
$n\pi + \frac{\pi }{3}$
C
$2n\pi \pm \frac{\pi }{3}$
D
None of these

✓

Answer

Correct option: A.

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

a
(a) $2\sin 3x\cos x - 2\sin 3x = 0$,

$\therefore $ $\sin 3x = 0$, $\cos x = 1$

$\Rightarrow 3x = n\pi $ or $x = \frac{{n\pi }}{3}$ and $x = 2n\pi $

The second value $x = 2n\pi $ is included in the value given by $x = \frac{{n\pi }}{3}$.

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