Learn how to solve problems step by step online. Prove the trigonometric identity (1+tan(x))/(1+cot(x))=sin(x)/cos(x). Start by simplifying the right side of the identity: \frac{\sin\left(x\right)}{\cos\left(x\right)}. Starting from the left-hand side (LHS) of the identity. 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.

Prove the trigonometric identity (1+tan(x))/(1+cot(x))=sin(x)/cos(x)