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

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$\frac{\csc\left(x\right)^2}{\cot\left(x\right)+\tan\left(x\right)}$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity (csc(x)^2)/(cot(x)+tan(x))=cos(x)/sin(x). Starting from the left-hand side (LHS) of the identity. Use the trigonometric identities: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)} and \displaystyle\cot\left(\theta\right)=\frac{\cos\left(\theta\right)}{\sin\left(\theta\right)}. Apply the trigonometric identity: \csc\left(\theta \right)^n=\frac{1}{\sin\left(\theta \right)^n}, where n=2. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.