COMEDK · Maths · 8. Trigonometric Ratios & Identities
\(4\left(1+\cos \dfrac{\pi}{8}\right)\left(1+\cos \dfrac{3 \pi}{8}\right)\left(1+\cos \dfrac{5 \pi}{8}\right)\left(1+\cos \dfrac{7 \pi}{8}\right) \text { is equal to }\)
- A 1
- B \(\dfrac{1}{8}\)
- C \(\dfrac{1}{4}\)
- D \(\dfrac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let the given expression be \(E = 4 \left(1 + \cos \dfrac{\pi}{8}\right) \left(1 + \cos \dfrac{3\pi}{8}\right) \left(1 + \cos \dfrac{5\pi}{8}\right) \left(1 + \cos \dfrac{7\pi}{8}\right)\). Using the identity \(\cos(\pi - \theta) = -\cos \theta\), we have…
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