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COMEDK · Maths · 8. Trigonometric Ratios & Identities

\(\cos ^{2} \frac{\pi}{12}+\cos ^{2} \frac{\pi}{4}+\cos ^{2} \frac{5 \pi}{12}=\)

  1. A \(\frac{3}{2}\)
  2. B \(\frac{3-\sqrt{3}}{2}\)
  3. C \(\frac{2}{3}\)
  4. D \(\frac{2}{3+\sqrt{3}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{3}{2}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \cos ^{2} \frac{\pi}{12}+\cos ^{2} \frac{\pi}{4}+\cos ^{2} \frac{5 \pi}{12} \\ =& \cos ^{2} \frac{\pi}{12}+\cos ^{2} \frac{\pi}{4}+\cos ^{2}\left(\frac{\pi}{2}-\frac{\pi}{12}\right) \\ =& \cos ^{2} \frac{\pi}{12}+\cos ^{2} \frac{\pi}{4}+\sin ^{2} \frac{\pi}{12}…