If 1,, + ,,sin theta ,, + ,,{sin ^2}thet | vedclass

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Question

${1+\sin 	heta+\sin ^{2} 	heta+\ldots \ldots=4+2 \sqrt{3}} $

${\Rightarrow \quad \frac{1}{1-\sin 	heta}=4+2 \sqrt{3}} $

${\Rightarrow \quad \

Vedclass · Accepted Answer

$\frac{\pi }{3}$ or $\frac{2\pi }{3}$

Vedclass · Answer

${1+\sin 	heta+\sin ^{2} 	heta+\ldots \ldots=4+2 \sqrt{3}} $

${\Rightarrow \quad \frac{1}{1-\sin 	heta}=4+2 \sqrt{3}} $

${\Rightarrow \quad \frac{1}{1-\sin 	heta}=\frac{1}{4+2 \sqrt{3}}} $

${\Rightarrow \quad 1-\sin 	heta=\frac{1}{2(2+\sqrt{3})(2-\sqrt{3})}} $

${=\frac{1}{2} \cdot \frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}} $

${=\frac{1}{2} \cdot \frac{2-\sqrt{3}}{4-3}=\frac{2-\sqrt{3}}{2}=1-\frac{\sqrt{3}}{2}}$

${\Rightarrow \quad \sin 	heta=\frac{\sqrt{3}}{2} \quad \Rightarrow 	heta=\frac{\pi}{6}}$

If $1\,\, + \,\,\sin \theta \,\, + \,\,{\sin ^2}\theta + \ldots .\,\,to\,\,\infty \,\, = \,\,4\, + 2\sqrt 3 ,\,\,0\,\, < \,\theta \,\,\pi ,\,\,\theta \,\, \ne \,\frac{\pi }{2}\,,$ then $\theta = $

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