Prove the trigonometric identity $\frac{\csc\left(\theta\right)-1}{\cot\left(\theta\right)}=\frac{\cot\left(\theta\right)}{\csc\left(\theta\right)+1}$

Learn how to solve limits by direct substitution problems step by step online. Prove the trigonometric identity (csc(t)-1)/cot(t)=cot(t)/(csc(t)+1). Starting from the right-hand side (RHS) of the identity. Multiply and divide the fraction \frac{\cot\left(\theta\right)}{\csc\left(\theta\right)+1} by the conjugate of it's denominator \csc\left(\theta\right)+1. Multiplying fractions \frac{\cot\left(\theta\right)}{\csc\left(\theta\right)+1} \times \frac{\csc\left(\theta\right)-1}{\csc\left(\theta\right)-1}. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2..