If sin 5x + sin 3x + sin x = 0, then the valu | vedclass

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Question

(c) $ \sin 5x + \sin 3x + \sin x = 0$

$ \Rightarrow $ $ - \sin 3x = \sin 5x + \sin x = 2\sin 3x\cos 2x$

$ \Rightarrow $ $\sin 3x = 0$

$ \Righ

Vedclass · Accepted Answer

$\frac{\pi }{3}$

Vedclass · Answer

(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.

If $\sin 5x + \sin 3x + \sin x = 0$, then the value of $x$ other than $0$ lying between $0 \le x \le \frac{\pi }{2}$ is

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