Question

If $1+\sin x+\sin ^{2} x+\quad$ upto $\infty$ $=4+2 \sqrt{3}, 0

• 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} $

Answer 1

Answer: (C)

Given, $1+\sin x+\sin ^{2} x+... \infty=4+2 \sqrt{3}$
$\Rightarrow \frac{1}{1-\sin x}=4+2 \sqrt{3}$
$\Rightarrow 1-\sin x=\frac{1}{4+2 \sqrt{3}} \times \frac{4-2 \sqrt{3}}{4-2 \sqrt{3}}$
$\frac{4-2 \sqrt{3}}{4}$
$\Rightarrow \sin x =\frac{2 \sqrt{3}}{4}=\frac{\sqrt{3}}{2}$
$\Rightarrow x =\frac{\pi}{3} \frac{2 \pi}{3}$