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

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)-2=sec(x)/tan(x)-2. Starting from the right-hand side (RHS) of the identity. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Simplify the fraction \frac{\frac{1}{\cos\left(x\right)}}{\frac{\sin\left(x\right)}{\cos\left(x\right)}}.