(c) $ \sin 5x + \sin 3x + \sin x = 0$

$ \Rightarrow $ $ – \sin 3x = \sin 5x + \sin x = 2\sin 3x\cos 2x$

$ \Rightarrow $ $\sin 3x = 0$

$ \Rightarrow $ $x = 0$

or $\cos 2x = – \frac{1}{2} = – \cos \,\left( {\frac{\pi }{3}} \right) = \cos \,\left( {\pi – \frac{\pi }{3}} \right)$

$ \Rightarrow $ $2x = 2n\pi \pm \left( {\pi – \frac{\pi }{3}} \right)\, $

$\Rightarrow x = n\pi \pm \left( {\frac{\pi }{3}} \right)$

For $x$ lying between $0$ and $\frac{\pi }{2}$, we get $x = \frac{\pi }{3}$.

Trick : Check with options.