Question

Find all values of $\theta$ satisfying the equation $\sin \theta =\sin \theta +\sin 3\theta ,$ where $0\le \theta \le \pi$

Answer 1

Given : $sin\theta =sin\theta +sin3\theta$

$sin3\theta =0$

$3\theta =n\pi$

$\theta =\frac{n\pi }{3}\to$ Now start putting value of 'n'

$n=0;\theta =0$

$n=1;\theta =\frac{\pi }{3}$

$n=2;\theta =\frac{2\pi }{3}$

$n=3;\theta =\pi$