AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\left(4 \cos ^2 \frac{\pi}{20}-1\right)\left(4 \cos ^2 \frac{3 \pi}{20}-1\right)\left(4 \cos ^2 \frac{5 \pi}{20}+1\right)\left(4 \cos ^2 \frac{7 \pi}{20}-1\right)\left(4 \cos ^2 \frac{9 \pi}{20}-1\right)=\)
- A \(1\)
- B \(\frac{1}{2}\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
Use identity: \(4\cos^2 x - 1 = \frac{\sin(3x)}{\sin x}\). Evaluate the third term: \(4\cos^2 \frac{5\pi}{20}+1 = 4\cos^2 \frac{\pi}{4}+1 = 4\left(\frac{1}{\sqrt{2}}\right)^2+1 = 4\left(\frac{1}{2}\right)+1 = 3\). Substitute into the expression:…
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