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AP EAMCET · Maths · Trigonometric Equations

\(1+\sin x+\sin ^2 x+\sin ^3 x+\ldots+\infty=4+2 \sqrt{3}\) and \(0 \lt x \lt \pi\), \(x \neq \frac{\pi}{2}\) then \(x=\)

  1. A \(\frac{\pi}{6}, \frac{\pi}{4}\)
  2. B \(\frac{\pi}{4}, \frac{5 \pi}{6}\)
  3. C \(\frac{2 \pi}{5}, \frac{\pi}{6}\)
  4. D \(\frac{\pi}{3}, \frac{2 \pi}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\pi}{3}, \frac{2 \pi}{3}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { Since, } 1+\sin x+\sin ^2 x+\sin ^3 x+\ldots=4+2 \sqrt{3} \\ \Rightarrow & \frac{1}{1-\sin x}=4+2 \sqrt{3} \Rightarrow 1-\sin x=\frac{1}{4+2 \sqrt{3}}\end{aligned}\)…