Let S, = ,left{ {theta , in ,[ - ,2,pi , | vedclass

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Question

$2\,(1 - {\sin ^2}	heta )\, + \,3\,\sin \,	heta \, = \,0$

$ \Rightarrow {\kern 1pt} 2\,{\sin ^2}	heta \, - \,3\sin \,	heta \, - \,2\, = \,0$

Vedclass · Accepted Answer

$2\pi $

Vedclass · Answer

$2\,(1 - {\sin ^2}	heta )\, + \,3\,\sin \,	heta \, = \,0$

$ \Rightarrow {\kern 1pt} 2\,{\sin ^2}	heta \, - \,3\sin \,	heta \, - \,2\, = \,0$

$ \Rightarrow (2\,\sin 	heta  + 1)(\sin 	heta  - 2) = 0$

$ \Rightarrow \sin 	heta \, = \, - \frac{1}{2};\,\,\,\sin 	heta  = 2$  (reject)

roots  :  $\pi \, + \,\frac{\pi }{6}\,,\,2\pi  - \frac{\pi }{6},\, - \frac{\pi }{6},\, - \pi  + \frac{\pi }{6}$

$\Rightarrow $ Sum off values $=\,2\pi $

Let $S\, = \,\left\{ {\theta \, \in \,[ - \,2\,\pi ,\,\,2\,\pi ]\, :\,2\,{{\cos }^2}\,\theta \, + \,3\,\sin \,\theta \, = \,0} \right\}$. Then the sum of the elements of $S$ is

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