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

Learn how to solve problems step by step online. Prove the trigonometric identity tan(x/2)=csc(x)-cot(x). Starting from the left-hand side (LHS) of the identity. Since the expression on the left of the equality is too simple, it's not clear how we can proceed to prove the identity from there. Although we know that the identity is true.