Answer
See the explanation below.
Work Step by Step
The left side in the given expression $\frac{\cot x-1}{\cot x+1}$ can be simplified by multiplying and dividing the expression by cot x. Therefore, the expression is simplified as:
$\frac{\cot x-1}{\cot x+1}=\frac{\frac{\cot x}{\cot x}-\frac{1}{\cot x}}{\frac{\cot x}{\cot x}+\frac{1}{\cot x}}$
We have the reciprocal identity, $\tan x=\frac{1}{\cot x}$ . Now, after applying the identity, the given expression can be further simplified as:
$\frac{\frac{\cot x}{\cot x}-\frac{1}{\cot x}}{\frac{\cot x}{\cot x}+\frac{1}{\cot x}}=\frac{1-\tan x}{1+\tan x}$
Hence, the left side is equal to the right side $\frac{\cot x-1}{\cot x+1}=\frac{1-\tan x}{1+\tan x}$.
