# How do you find the numerical value of one trigonometric function of x if tan x/cot x - sec x/cos x = 2/csc x ???

Apr 14, 2018

210 degree

#### Explanation:

Given, $\frac{\tan x}{\cot x} - \frac{\sec x}{\cos x} = \frac{2}{\csc} x$
$\Rightarrow \tan \frac{x}{\frac{1}{\tan} x} - \frac{\sec}{\frac{1}{\sec} x} = 2 \sin x$
$\Rightarrow {\tan}^{2} x - {\sec}^{2} x = 2 \sin x$[As sec^2x-tan^2x = 1]
$\Rightarrow - 1 = 2 \sin x$
$\Rightarrow \sin x = - \frac{1}{2}$
$\Rightarrow \sin x = \sin \left(180 + 30\right)$
$\Rightarrow x = 210$