A) \[\frac{\pi }{3},\frac{5\pi }{6}\]
B) \[\frac{2\pi }{3},\frac{\pi }{6}\]
C) \[\frac{\pi }{3},\frac{2\pi }{3}\]
D) \[\frac{\pi }{6},\frac{\pi }{3}\]
Correct Answer: C
Solution :
Given, \[1+\sin x+{{\sin }^{2}}x+....\infty =4+2\sqrt{3}\] \[\Rightarrow \] \[\frac{1}{1-\sin x}=4+2\sqrt{3}\] \[\Rightarrow \] \[1-\sin x=\frac{1}{4+2\sqrt{3}}\times \frac{4-2\sqrt{3}}{4-2\sqrt{3}}\] \[\Rightarrow \] \[1-\sin x=\frac{4-2\sqrt{3}}{4}\] \[\Rightarrow \] \[\sin x=\frac{2\sqrt{3}}{4}=\frac{\sqrt{3}}{2}\] \[\Rightarrow \] \[x=\frac{\pi }{3},\frac{2\pi }{3}\]
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