JEE Main 2026 — 5 April, Evening Shift — Question 46

$\cos \theta \cos \frac{5 \theta}{2}=\cos 7 \theta \cos \frac{7 \theta}{2}$ $\cos \frac{7 \theta}{2}+\cos \frac{3 \theta}{2}=\cos \frac{21 \theta}{2}+\cos \frac{7 \theta}{2}$ $\cos \frac{21 \theta}{2}-\cos \frac{3 \theta}{2}=0$ $-2 \sin 6 \theta \sin \frac{9 \theta}{2}=0$ $\sin 6 \theta=0$ $\theta=0, \pm \frac{\pi}{6}, \pm \frac{2 \pi}{6}, \ldots \pm \frac{5 \pi}{6}, \pm \pi \quad$ (13 solutions) $\sin \frac{9 \theta}{2}=0$ $\theta= \pm \frac{2 \pi}{9}, \pm \frac{4 \pi}{9}, \pm \frac{8 \pi}{9} \quad(6$ more solutions $)$ Total $= 19$ solutions