Question

termine the non-permissible values for the equation \\(\frac{\tan x cos x}{csc x} = 1 - cos^2 x\\)

Explanation:

Step1: Identify undefined trigonometric terms

Recall that $\tan x = \frac{\sin x}{\cos x}$, $\csc x = \frac{1}{\sin x}$. These are undefined when their denominators are 0.

• $\cos x = 0$ when $x = \frac{\pi}{2} + n\pi$, $n\in\mathbb{Z}$
• $\sin x = 0$ when $x = n\pi$, $n\in\mathbb{Z}$

Step2: Combine non-permissible values

Combine the values where either $\cos x=0$ or $\sin x=0$, as these make the left-hand side of the equation undefined.

Answer:

$x = \frac{n\pi}{2}$, where $n$ is any integer