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

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$\frac{\tan\left(x\right)+\sec\left(x\right)}{\sec\left(x\right)-\cos\left(x\right)+\tan\left(x\right)}$

Learn how to solve problems step by step online. Prove the trigonometric identity (tan(x)+sec(x))/(sec(x)-cos(x)tan(x))=csc(x). Starting from the left-hand side (LHS) of the identity. Rewrite \tan\left(x\right)+\sec\left(x\right) in terms of sine and cosine functions. Rewrite \sec\left(x\right)-\cos\left(x\right)+\tan\left(x\right) in terms of sine and cosine functions. Simplify the fraction \frac{\frac{\sin\left(x\right)+1}{\cos\left(x\right)}}{\frac{1-\cos\left(x\right)^2+\sin\left(x\right)}{\cos\left(x\right)}}.