The number of solutions of the equation sin ( | vedclass

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Question

(b)

Given trigonometric equation is

$\sin (9 x)+\sin (3 x)=0$

$\Rightarrow \quad 2 \sin 6 x \cos 3 x=0$

$	herefore \quad$ either $\sin 6

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(b)

Given trigonometric equation is

$\sin (9 x)+\sin (3 x)=0$

$\Rightarrow \quad 2 \sin 6 x \cos 3 x=0$

$	herefore \quad$ either $\sin 6 x=0$

or $\quad \cos 3 x=0$

for $x \in[0,2 \pi]$

$\sin 6 x=0$

$\Rightarrow \quad x=0, \frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{5 \pi}{6}$,

and $3 x=0$

$\Rightarrow \quad x=\frac{\pi}{6}, \frac{\pi}{2}, \frac{5 \pi}{6}, \frac{7 \pi}{6}, \frac{3 \pi}{2}, \frac{11 \pi}{6}$

So, number of solution of given equation is $13$

The number of solutions of the equation $\sin (9 x)+\sin (3 x)=0$ in the closed interval $[0,2 \pi]$ is

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