17. The equation $\cos 15 \theta=\cos 3 \theta$ has $(\quad)$ roots in $\left[0,180^{\circ}\right]$.
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
17. C.

Let $x=3 \theta$. Then the problem becomes finding how many $x \in[0,3 \pi]$, such that $\cos 5 x=\cos x$. This equation holds if and only if there exists an integer $k$, such that $5 x=2 k \pi \pm x$, i.e.,
$$
x=\frac{k \pi}{2} \text { or } x=\frac{k \pi}{3} \text {. }
$$

When $x$ is an integer multiple of $\pi$, it satisfies both equations, and there are 4 values in $[0,3 \pi]$. When $x$ is not an integer multiple of $\pi$, there are 3 values in $[0,3 \pi]$ that satisfy $x=\frac{k \pi}{2}$, and 6 values in $[0,3 \pi]$ that satisfy $x=\frac{k \pi}{3}$. Therefore, $4+3+6=13$.