Question

Solve the following equation:
$\sec x+\text{cosec}x=2\sqrt{2}$

Answer 1

$\sin x+\cos x=\sqrt{2}\sin 2x$

$\cos (x-\frac{\pi }{4})=\cos (2n\pi +\frac{\pi }{2}-2n)$

$x-\frac{\pi }{4}=2n\pi +\frac{\pi }{2}-2n$

$x=2n\frac{\pi }{3}+\frac{\pi }{4}.$