# How do I solve 2(sin x-cos x)=3(sin x+cos x) ?

Jul 3, 2018

$x = 1.76 , 4.91$

#### Explanation:

$2 \left(\sin x - \cos x\right) = 3 \left(\sin x + \cos x\right)$

$2 \sin x - 2 \cos x = 3 \sin x + 3 \cos x$

$- 5 \cos x = \sin x$

$\tan x = - 5$

If in the region of $0$ and $2 \pi$ ie $0 \le x \le 2 \pi$

$x = 1.76 , 4.91$