Prove the trigonometric identity $\frac{\cot\left(x\right)^2}{\csc\left(x\right)^2}=\cos\left(x\right)^2$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity (cot(x)^2)/(csc(x)^2)=cos(x)^2. Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: \cot(x)=\frac{\cos(x)}{\sin(x)}. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. We can simplify the quotient of fractions \frac{\frac{\cos\left(x\right)^2}{\sin\left(x\right)^2}}{\frac{1}{\sin\left(x\right)^2}} by inverting the second fraction and multiply both fractions.