One of the solutions of the equation 8 sin ^3 | vedclass

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Question

(b)

Given,

$8 \sin ^3 	heta-7 \sin 	heta+\sqrt{3} \cos 	heta =0$

$2\left(4 \sin ^3 	hetaight)-7 \sin 	heta+\sqrt{3} \cos 	heta =0$

Vedclass · Accepted Answer

$\left(10^{\circ}, 20^{\circ}\right)$

Vedclass · Answer

(b)

Given,

$8 \sin ^3 	heta-7 \sin 	heta+\sqrt{3} \cos 	heta =0$

$2\left(4 \sin ^3 	hetaight)-7 \sin 	heta+\sqrt{3} \cos 	heta =0$

$2(3 \sin 	heta-\sin 3 	heta)-7 \sin 	heta$

$+\sqrt{3} \cos 	heta =0$

$6 \sin 	heta-2 \sin 3 	heta-7 \sin 	heta$

$+\sqrt{3} \cos 	heta =0$

$\sqrt{3} \cos 	heta-\sin 	heta-2 \sin 3 	heta =0$

$\frac{\sqrt{3}}{2} \cos 	heta-\frac{1}{2} \sin 	heta =\sin 3 	heta$

$\sin \left(\frac{\pi}{3}-	hetaight) =\sin 3 	heta$

$\frac{\pi}{3}-	heta=3 	heta \Rightarrow 4 	heta=60^{\circ} \Rightarrow 	heta =15^{\circ}$

$	heta \in\left(10^{\circ}, 20^{\circ}ight]$

One of the solutions of the equation $8 \sin ^3 \theta-7 \sin \theta+\sqrt{3} \cos \theta=0$ lies in the interval

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