Final Answer
Step-by-step Solution
Specify the solving method
Starting from the left-hand side (LHS) of the identity
Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{1}{\tan\left(\theta \right)}$
Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{1}{\tan\left(\theta \right)}$
Combine all terms into a single fraction with $\tan\left(x\right)$ as common denominator
Combine all terms into a single fraction with $\tan\left(x\right)$ as common denominator
Simplify the fraction $\frac{\frac{1-\tan\left(x\right)^2}{\tan\left(x\right)}}{\frac{1+\tan\left(x\right)}{\tan\left(x\right)}}$
Factor the difference of squares $1-\tan\left(x\right)^2$ as the product of two conjugated binomials
Simplify the fraction $\frac{\left(1+\tan\left(x\right)\right)\left(1-\tan\left(x\right)\right)}{1+\tan\left(x\right)}$ by $1+\tan\left(x\right)$
Since we have reached the expression of our goal, we have proven the identity