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Question Number 32968 by diyatrivedi last updated on 08/Apr/18

Answered by MJS last updated on 08/Apr/18

$$\frac{\sin \alpha }{\sin \theta }=\cos \alpha \times \cos \theta +\sin \alpha \times \sin \theta$$$$\sin \alpha =\cos \alpha \times \cos \theta \times \sin \theta +\sin \alpha \times {\sin }^2\theta$$$$\sin \alpha =\cos \alpha \times \frac{\sin 2\theta }{2}+\sin \alpha \times \left(\frac{1-\cos 2\theta }{2}\right)$$$$\frac{\sin \alpha }{2}=\cos \alpha \times \frac{\sin 2\theta }{2}-\sin \alpha \times \frac{\cos 2\theta }{2}$$$$\sin \alpha =\frac{\sin (2\theta +\alpha )+\sin (2\theta -\alpha )}{2}-\frac{\sin (\alpha +2\theta )+\sin (\alpha -2\theta )}{2}$$$$\sin \alpha =\sin (2\theta -\alpha )$$$$\alpha =\theta +n\pi [\theta \in \mathbb{R};n\in \mathbb{Z}]$$$$\mathrm{or}$$$$\theta =\frac{\pi }{2}+n\pi [\alpha \in \mathbb{R};n\in \mathbb{Z}]$$

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