TS EAMCET · Maths · Trigonometric Ratios & Identities
\(\cos \frac{2 \pi}{7}+\cos \frac{4 \pi}{7}+\cos \frac{6 \pi}{7}+\cos \frac{7 \pi}{7}\) is equal to
- A \(\frac{1}{2}\)
- B 1
- C \(\frac{-1}{2}\)
- D \(\frac{-3}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{-3}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \cos \frac{2 \pi}{7}+\cos \frac{4 \pi}{7}+\cos \frac{6 \pi}{7}+\cos \frac{7 \pi}{7} \\ & =\cos \frac{2 \pi}{7}+\cos \frac{4 \pi}{7}+\cos \frac{6 \pi}{7}-1 \\ & =\frac{1}{2 \sin \frac{\pi}{7}}\left[2 \sin \frac{\pi}{7} \cdot \cos \frac{2 \pi}{7}+2 \cos \frac{4…
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