TS EAMCET · Maths · Trigonometric Ratios & Identities
The period of \(\frac{\sin x}{\cos 3 x}+\frac{\sin 3 x}{\cos 9 x}+\frac{\sin 9 x}{\cos 27 x}+\frac{\sin 27 x}{\cos 81 x}\) is
- A \(\frac{2 \pi}{3}\)
- B \(\frac{\pi}{81}\)
- C \(2 \pi\)
- D \(\pi\)
Answer & Solution
Correct Answer
(D) \(\pi\)
Step-by-step Solution
Detailed explanation
Given, \(\frac{\sin x}{\cos 3 x}+\frac{\sin 3 x}{\cos 9 x}+\frac{\sin 9 x}{\cos 27 x}+\frac{\sin 27 x}{\cos 81 x}\) \(=\frac{1}{2}\left[\frac{2 \sin x \cos x}{\cos 3 x \cos x}+\frac{2 \sin 3 x \cos 3 x}{\cos 9 x \cos 3 x}+\frac{2 \sin 9 x \cos 9 x}{\cos 27 x \cos 9 x}\right.\)…
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