JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 88

$\cos x+\cos4x+\cos2x+\cos3x=4\cos\frac{5x}2\cos x\cos\frac x2$. In $[0,2\pi)$: $\cos\frac{5x}2=0$ at $x=\frac\pi5,\frac{3\pi}5,\pi,\frac{7\pi}5,\frac{9\pi}5$; $\cos x=0$ at $\frac\pi2,\frac{3\pi}2$; $\cos\frac x2=0$ at π (already counted). That is 7 values.