Question

$\cos \theta +\cos 7\theta +\cos 3\theta +\cos 5\theta =0$ Find the value of $\theta$.

Answer 1

Combining $\theta$ and $7\theta ,3\theta$ and $5\theta$, we get
$2\cos 4\theta (\cos 3\theta +\cos \theta )=0$
$\therefore 4\cos 4\theta \cos 2\theta \cos \theta =0$
or $4\cdot \frac{1}{2^3\sin \theta }\left(\sin 2^3\theta \right)=$
or $\sin 8\theta =0$
$\therefore \theta =n\pi /8$.