If $3 \sin heta=2 \sin 3 heta$ and $0

Question

If $3 \sin 	heta=2 \sin 3 	heta$ and $0 < 	heta < \pi$, then $\sin 	heta=$

Aicharya · Accepted Answer

$\begin{aligned} & 3 \sin 	heta=2 \sin 3 	heta \ & \quad=2\left(3 \sin 	heta-4 \sin ^2 	hetaight) \ & 	herefore 8 \sin ^3 	heta-3 \sin 	heta=0 \ & 	herefore \sin 	heta\left(8 \sin ^2 	heta-3ight)=0 \ & 	herefore \sin 	heta=0 	ext { or } \sin 	heta= \pm \sqrt{\frac{3}{8}}= \pm \frac{\sqrt{3}}{2 \sqrt{2}} \end{aligned}$ Since, $0 < 	heta < \pi$, we write $\sin 	heta=\frac{\sqrt{3}}{2 \sqrt{2}}$

If $3 \sin \theta=2 \sin 3 \theta$ and $0 < \theta < \pi$, then $\sin \theta=$

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