Learn how to solve integrals of exponential functions problems step by step online. Prove the trigonometric identity 1/(csc(x)+cot(x))=csc(x)-cot(x). Starting from the left-hand side (LHS) of the identity. Multiply and divide the fraction \frac{1}{\csc\left(x\right)+\cot\left(x\right)} by the conjugate of it's denominator \csc\left(x\right)+\cot\left(x\right). Multiplying fractions \frac{1}{\csc\left(x\right)+\cot\left(x\right)} \times \frac{\csc\left(x\right)-\cot\left(x\right)}{\csc\left(x\right)-\cot\left(x\right)}. 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..

Prove the trigonometric identity 1/(csc(x)+cot(x))=csc(x)-cot(x)