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AP EAMCET · Maths · Trigonometric Ratios & Identities

The value of \(\sin \left(\frac{5 \pi}{24}\right) \cdot \cos \left(\frac{\pi}{24}\right)\) is

  1. A \(\frac{1+\sqrt{2}}{4}\)
  2. B \(1+\sqrt{2}\)
  3. C \(\frac{1-\sqrt{2}}{4}\)
  4. D \(1-\sqrt{2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1+\sqrt{2}}{4}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \sin \left(\frac{5 \pi}{24}\right) \cdot \cos \left(\frac{\pi}{24}\right) \\ & =\frac{1}{2}\left[\sin \left(\frac{5 \pi}{24}+\frac{\pi}{24}\right)+\sin \left(\frac{5 \pi}{24}-\frac{\pi}{24}\right)\right] \\ & =\frac{1}{2}\left[\sin…