The values of theta satisfying sin 7theta = | vedclass

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Question

(a) $\sin 7	heta + \sin 	heta - \sin 4	heta = 0$

$ \Rightarrow $ $2\sin 4	heta \cos 3	heta - \sin 4	heta = 0$

$ \Rightarrow $ $\sin 4	het

Vedclass · Accepted Answer

$\frac{\pi }{9},\frac{\pi }{4}$

Vedclass · Answer

(a) $\sin 7	heta + \sin 	heta - \sin 4	heta = 0$

$ \Rightarrow $ $2\sin 4	heta \cos 3	heta - \sin 4	heta = 0$

$ \Rightarrow $ $\sin 4	heta (2\cos 3	heta - 1) = 0 $

$\Rightarrow \sin 4	heta = 0,\,{m{ }}\cos 3	heta = \frac{1}{2}$

Now $\sin 4	heta = 0$ $ \Rightarrow $ $4	heta = \pi $ $ \Rightarrow $ $	heta = \frac{\pi }{4}$.

and $\cos 3	heta = \frac{1}{2}$ $ \Rightarrow $ $3	heta = \frac{\pi }{3}$ $ \Rightarrow $ $	heta = \frac{\pi }{9}$.

The values of $\theta $ satisfying $\sin 7\theta = \sin 4\theta - \sin \theta $ and $0 < \theta < \frac{\pi }{2}$ are

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