TS EAMCET · Maths · Trigonometric Ratios & Identities
\(1+\cos x+\cos ^2 x+\cos ^3 x+\ldots\) to \(\infty=4+2 \sqrt{3}\), then \(x=\)
- A \(\frac{n \pi}{6}\)
- B \((4 n \pm 1) \frac{\pi}{3}\)
- C \((12 n \pm 1) \frac{\pi}{6}\)
- D \((3 n \pm 1) \frac{\pi}{3}\)
Answer & Solution
Correct Answer
(C) \((12 n \pm 1) \frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{1-\cos x}=4+2 \sqrt{3}\) \(1-\cos x=\frac{1}{4+2 \sqrt{3}} = \frac{4-2 \sqrt{3}}{16-12} = \frac{4-2 \sqrt{3}}{4} = 1-\frac{\sqrt{3}}{2}\) \(\cos x=\frac{\sqrt{3}}{2}\) \(x=2n\pi \pm \frac{\pi}{6}\) \(x=(12n \pm 1)\frac{\pi}{6}\)
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