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

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