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AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\sin \frac{\pi}{16} \sin \frac{3 \pi}{16} \sin \frac{5 \pi}{16} \sin \frac{7 \pi}{16}\) is equal to

  1. A \(\frac{\sqrt{2}}{16}\)
  2. B \(\frac{1}{8}\)
  3. C \(\frac{1}{16}\)
  4. D \(\frac{\sqrt{2}}{32}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\sqrt{2}}{16}\)

Step-by-step Solution

Detailed explanation

We have, \(\sin \frac{\pi}{16} \sin \frac{3 \pi}{16} \sin \frac{5 \pi}{16} \sin \frac{7 \pi}{16}\) \(=\sin \frac{\pi}{16} \sin \frac{3 \pi}{16} \sin \left(\frac{\pi}{2}-\frac{3 \pi}{16}\right) \sin \left(\frac{\pi}{2}-\frac{\pi}{16}\right)\)…