यदि sin theta + sin 2theta + sin | vedclass

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Question

$\sin 	heta  + \sin \,3	heta  + \sin \,2	heta  = \sin \,\alpha $

$2\sin 2	heta \cos 	heta  + \sin 2	heta  = \sin \al

Vedclass · Accepted Answer

$\alpha /2$

Vedclass · Answer

$\sin 	heta  + \sin \,3	heta  + \sin \,2	heta  = \sin \,\alpha $

$2\sin 2	heta \cos 	heta  + \sin 2	heta  = \sin \alpha $

$\sin 2	heta (2\cos 	heta  + 1) = \sin \alpha $&hellip;..$(i)$

अब $\cos 	heta  + \cos 3	heta  + \cos 2	heta  = \cos \alpha $

$2\cos 2\,	heta \cos \,	heta  + \cos 2	heta  = \cos \alpha $

$\cos 2	heta \,(2\cos 	heta  + 1) = \cos \alpha $&hellip;..$(ii)$

समीकरण $(i)$ एवं $(ii)$ से,

$	an 2	heta  = 	an \alpha $

$\Rightarrow$  $2	heta  = \alpha $

$\Rightarrow$  $	heta  = \alpha /2$.

यदि $\sin \theta + \sin 2\theta + \sin 3\theta = \sin \alpha $ तथा $\cos \theta + \cos 2\theta + \cos 3\theta = \cos \alpha $, तब $\theta$ का मान होगा

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