# How do I solve for the equation 0 ≤ x < 2π √2 tan x = 2 sin x ?

Feb 22, 2018

$x = \frac{\pi}{4} , \frac{7}{4} \pi$

#### Explanation:

$\sqrt{2} \tan x = 2 \sin$

$\tan \frac{x}{\sin} x = \frac{2}{\sqrt{2}}$

$\frac{1}{\cos} x = \sqrt{2}$

note:
$\tan \frac{x}{\sin} x = \tan x \div \sin x = \sin \frac{x}{\cos} x \div \sin x = \frac{\cancel{\sin x}}{\cos} x \cdot \frac{1}{\cancel{\sin x}} = \frac{1}{\cos} x$

$\cos x = \frac{1}{\sqrt{2}}$

$x = \frac{\pi}{4} , \frac{7}{4} \pi$