JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of solutions of the equation \(\cos 2 \theta \cos \frac{\theta}{2}+\cos \frac{5 \theta}{2}=2 \cos ^3 \frac{5 \theta}{2}\) in \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) is :
- A 7
- B 5
- C 6
- D 9
Answer & Solution
Correct Answer
(A) 7
Step-by-step Solution
Detailed explanation
\begin{aligned} & \cos 2 \theta \cos \frac{\theta}{2}+\cos \frac{5 \theta}{2}=2 \cos ^3 \frac{5 \theta}{2} \\ & \frac{1}{2}\left(2 \cos 2 \theta \cos \frac{\theta}{2}\right)+\cos \frac{50}{2} \\ & =\frac{1}{2}\left(\cos \frac{15 \theta}{2}+3 \cos \frac{5 \theta}{2}\right)…
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