JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
The value of \( \cos ^{3}\left(\frac{\pi}{8}\right) \cdot \cos \left(\frac{3 \pi}{8}\right)+\sin ^{3}\left(\frac{\pi}{8}\right) \cdot \sin \left(\frac{3 \pi}{8}\right)\) is
- A \(\frac{1}{4}\)
- B \(\frac{1}{\sqrt{2}}\)
- C \(\frac{1}{2\sqrt{2}}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\(\cos ^{3} \frac{\pi}{8} \cdot \sin \frac{\pi}{8}+\sin ^{3} \frac{\pi}{8} \cdot \cos \frac{\pi}{8}\) \(=\sin \frac{\pi}{8} \cdot \cos \frac{\pi}{8}=\frac{1}{2} \sin \frac{\pi}{4}=\frac{1}{2 \sqrt{2}}\)
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