JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(S = \left\{\theta \in [-\pi, \pi] : \cos\theta \cos\dfrac{5\theta}{2} = \cos 7\theta \cos\dfrac{7\theta}{2}\right\}\), then \(n(S)\) is equal to _______.
- A 19
- B 22
- C 26
- D 28
Answer & Solution
Correct Answer
(A) 19
Step-by-step Solution
Detailed explanation
Given equation: \(\cos\theta \cos\dfrac{5\theta}{2} = \cos 7\theta \cos\dfrac{7\theta}{2}\) Multiplying both sides by \(2\): \(2\cos\theta \cos\dfrac{5\theta}{2} = 2\cos 7\theta \cos\dfrac{7\theta}{2}\) Using the identity \(2\cos A \cos B = \cos(A+B) + \cos(A-B)\):…
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