TS EAMCET · Maths · Trigonometric Ratios & Identities
\[ \cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7} \cos \frac{\pi}{14} \cos \frac{3 \pi}{14} \cos \frac{5 \pi}{14}= \]
- A \(\frac{1}{16}\left[\sin \frac{\pi}{7}+\sin \frac{2 \pi}{7}+\sin \frac{3 \pi}{7}\right]\)
- B \(\frac{1}{8}\left[\sin \frac{2 \pi}{7}+\sin \frac{3 \pi}{7}-\sin \frac{\pi}{7}\right]\)
- C \(\frac{1}{32}\left[\sin \frac{2 \pi}{7}+\sin \frac{3 \pi}{7}-\sin \frac{\pi}{7}\right]\)
- D \(\frac{1}{32}\left[\sin \frac{\pi}{7}-\sin \frac{2 \pi}{7}+\sin \frac{3 \pi}{7}\right]\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{32}\left[\sin \frac{2 \pi}{7}+\sin \frac{3 \pi}{7}-\sin \frac{\pi}{7}\right]\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {}\left(\cos \frac{\pi}{7}, \cos \frac{2 \pi}{7}, \cos \frac{3 \pi}{7}\right) \cos \frac{\pi}{14} \cdot \cos \frac{3 \pi}{14} \cdot \cos \frac{5 \pi}{14} \\ & =\left(\frac{2 \sin \frac{\pi}{7} \cdot \cos \frac{\pi}{7} \cdot \cos \frac{2 \pi}{7} \cdot \cos…
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