AP EAMCET · Maths · Trigonometric Ratios & Identities
The value of \(\sin \left(\frac{5 \pi}{24}\right) \cdot \cos \left(\frac{\pi}{24}\right)\) is
- A \(\frac{1+\sqrt{2}}{4}\)
- B \(1+\sqrt{2}\)
- C \(\frac{1-\sqrt{2}}{4}\)
- D \(1-\sqrt{2}\)
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…
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