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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(\theta\) is an acute angle and \(2 \sin ^2 \theta\) \(=\cos ^4 \frac{\pi}{8}+\sin ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\sin ^4 \frac{7 \pi}{8}\), then \(\theta=\)

  1. A \(\frac{\pi}{6}\)
  2. B \(\frac{\pi}{4}\)
  3. C \(\frac{\pi}{3}\)
  4. D \(\frac{\pi}{8}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\pi}{3}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \sin ^4\left(\frac{7 \pi}{8}\right)=\sin ^4\left(\pi-\frac{\pi}{8}\right)=\sin ^4\left(\frac{\pi}{8}\right) \\ & \cos ^4\left(\frac{5 \pi}{8}\right)=\cos ^4\left(\pi-\frac{3 \pi}{8}\right)=\cos ^4\left(\frac{3 \pi}{8}\right) \\ & \cos…