Prove the trigonometric identity $\frac{\cos\left(x\right)}{\sin\left(x\right)\cot\left(x\right)}=1$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity cos(x)/(sin(x)cot(x))=1. Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Multiplying the fraction by \sin\left(x\right). Simplify the fraction \frac{\cos\left(x\right)\sin\left(x\right)}{\sin\left(x\right)} by \sin\left(x\right).