Prove the trigonometric identity $\tan\left(x\right)\csc\left(x\right)-\sec\left(x\right)=0$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)csc(x)-sec(x)=0. Starting from the left-hand side (LHS) of the identity. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Multiplying fractions \frac{\sin\left(x\right)}{\cos\left(x\right)} \times \frac{1}{\sin\left(x\right)}.