Solve the following equation:
$sin x + sin 2 x + sin 3 x = 0$

Open in App

Solution

$sin x + sin 2 x + sin 3 x = 0$
$2 sin 2 x cos x + sin 2 x = 0$
$sin 2 x (2 cos x + 1) = 0$
either, $sin 2 x = 0$
$2 x = n π, x = n \frac{π}{2} .$
or, $cos x = - \frac{1}{2}$
$x = 2 n π \pm \frac{2 π}{3} .$

Suggest Corrections

Similar questions

sin x + sin 2 x + sin 3 x = cos x + cos 2 x + cos 3 x .

sin x - sin 2 x + sin 5 x + sin 8 x = 0.

a s i n \frac{x}{2} - (s i n x + s i n \frac{3 x}{2}) = 0.

\cos x + \cos 2 x + \cos 3 x = 0

\cos x + \cos 3 x - \cos 2 x = 0

\sin x + \sin 5 x = \sin 3 x

\cos x \cos 2 x \cos 3 x = \frac{1}{4}

\cos x + \sin x = \cos 2 x + \sin 2 x

\sin x + \sin 2 x + \sin 3 = 0

\sin x + \sin 2 x + \sin 3 x + \sin 4 x = 0

\sin 3 x - \sin x = 4 \cos^{2} x - 2

\sin 2 x - \sin 4 x + \sin 6 x = 0

1 - sin 2 x = cos x - sin x

Join BYJU'S Learning Program