The general solution of $\cos 2\theta\cos\left(\dfrac{\theta}{2}\right)=\cos\left(\dfrac{3\theta}{2}\right)$ is
Step-by-Step Solution
Key Concept: Use product-to-sum: $\cos 2\theta\cos(\theta/2)=\frac{1}{2}[\cos(5\theta/2)+\cos(3\theta/2)]$
$\cos(5\theta/2)=\cos(3\theta/2)\Rightarrow 5\theta/2=\pm3\theta/2+2n\pi$. Case 1: $\theta=n\pi$; Case 2: $4\theta=2n\pi\Rightarrow\theta=n\pi/2$. General: $\theta=n\pi/2$.
Correct Answer: 3