If cos 7theta = cos theta - sin 4theta,then t | vedclass

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(C) Given equation: $\cos 7	heta = \cos 	heta - \sin 4	heta$Rearranging the terms: $\sin 4	heta = \cos 	heta - \cos 7	heta$Using the formula $\c

Vedclass · Accepted Answer

$\frac{n\pi}{4}, \frac{n\pi}{3} + (-1)^n \frac{\pi}{18}$

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(C) Given equation: $\cos 7	heta = \cos 	heta - \sin 4	heta$Rearranging the terms: $\sin 4	heta = \cos 	heta - \cos 7	heta$Using the formula $\cos C - \cos D = 2 \sin \frac{C+D}{2} \sin \frac{D-C}{2}$:$\sin 4	heta = 2 \sin \frac{	heta + 7	heta}{2} \sin \frac{7	heta - 	heta}{2}$$\sin 4	heta = 2 \sin 4	heta \sin 3	heta$$\sin 4	heta (1 - 2 \sin 3	heta) = 0$Case $1$: $\sin 4	heta = 0$ $\Rightarrow 4	heta = n\pi$ $\Rightarrow 	heta = \frac{n\pi}{4}$Case $2$: $1 - 2 \sin 3	heta = 0 \Rightarrow \sin 3	heta = \frac{1}{2} = \sin \frac{\pi}{6}$Using the general solution $\sin x = \sin \alpha \Rightarrow x = n\pi + (-1)^n \alpha$:$3	heta = n\pi + (-1)^n \frac{\pi}{6} \Rightarrow 	heta = \frac{n\pi}{3} + (-1)^n \frac{\pi}{18}$Thus,the general values are $	heta = \frac{n\pi}{4}, \frac{n\pi}{3} + (-1)^n \frac{\pi}{18}$.

If $\cos 7\theta = \cos \theta - \sin 4\theta$,then the general value of $\theta$ is

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