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 :

[JEE Main 2025, 7 Apr (Shift 2)]

Question

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 :

[JEE Main 2025, 7 Apr (Shift 2)]

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The number of solutions of the equation \(\cos 2\theta \cos \frac{\theta }{2}+\cos \frac{5\theta }{2}=2{\cos }^{3}\frac{…

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