JEE Advanced 2017 · Paper 2, Mathematics question 12

Expand along row 1.
$$f=\cos2x(\cos^2x+\sin^2x)-\cos2x(\sin^2x-\cos^2x)-\sin2x(2\sin x\cos x)=\cos2x+\cos4x.$$

Stationary points.
$$f'(x)=-2\sin2x(1+4\cos2x).$$
In $(-\pi,\pi)$:

• $\sin2x=0$ at $x=0,\pm\frac\pi2$;
• $\cos2x=-\frac14$ at four more points.

That is seven points, more than three. (B) is true.

Maximum. $f\le2$, with equality at $x=0$. (C) is true.

(B), (C)