# How do you find cos 2x, given cot x = 3/5 and csc x < 0?

Dec 5, 2015

$- \frac{8}{17}$

#### Explanation:

$\cos \frac{x}{\sin} x = \frac{3}{5}$

$\frac{1 - {\sin}^{2} x}{\sin} ^ 2 x = \frac{9}{25}$

$9 {\sin}^{2} x = 25 - 25 {\sin}^{2} x$

sin x = ± sqrt{ 25/34}

$\frac{1}{\sin} x < 0 R i g h t a r r o w \sin x = - \frac{5}{\sqrt{34}}$

$\cos 2 x = \left(1 - {\sin}^{2} x\right) - {\sin}^{2} x = 1 - 2 \cdot \frac{25}{34}$