Question

Solve $sec4\theta -sec2\theta =2$.

Answer 1

$\frac{1}{\cos 4\theta }-\frac{1}{\cos 2\theta }=2$
$\cos 4\theta \ne 0,\cos 2\theta \ne 0$ .$\left(1\right)$
$\therefore \cos 2\theta -\cos 4\theta =2\cos 2\theta \cos 4\theta$
$=\cos 2\theta +\cos 6\theta$
$\therefore \cos 6\theta +\cos 4\theta =0$
or $2\cos 5\theta \cos \theta =0$
$\cos \theta =0=\cos \left(\pi /2\right)$ $\therefore \theta =n\pi +\pi /2$
$\cos 5\theta =0=\cos \left(\pi /2\right)$ $\therefore 5\theta =n\pi +\pi /2$
or $\theta =\frac{n\pi }{5}+\frac{\pi }{10}$.