Prove the trigonometric identity $\frac{\csc\left(x\right)^4-1}{\cot\left(x\right)^2}=2+\cot\left(x\right)^2$

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$\frac{\csc\left(x\right)^4-1}{\cot\left(x\right)^2}$

Learn how to solve product rule of differentiation problems step by step online. Prove the trigonometric identity (csc(x)^4-1)/(cot(x)^2)=2+cot(x)^2. Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: \cot\left(\theta \right)^2 = \csc\left(\theta \right)^2-1. Factor the difference of squares \csc\left(x\right)^4-1 as the product of two conjugated binomials. Simplify the fraction \frac{\left(\csc\left(x\right)^{2}+1\right)\left(\csc\left(x\right)^{2}-1\right)}{\csc\left(x\right)^2-1} by \csc\left(x\right)^{2}-1.