Prove the trigonometric identity $\frac{1+\cos\left(x\right)}{1-\cos\left(x\right)}=\frac{\sec\left(x\right)+1}{\sec\left(x\right)-1}$

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$\frac{\sec\left(x\right)+1}{\sec\left(x\right)-1}$

Learn how to solve integrals involving logarithmic functions problems step by step online. Prove the trigonometric identity (1+cos(x))/(1-cos(x))=(sec(x)+1)/(sec(x)-1). Starting from the right-hand side (RHS) of the identity. Rewrite \frac{\sec\left(x\right)+1}{\sec\left(x\right)-1} in terms of sine and cosine functions. Combine all terms into a single fraction with \cos\left(x\right) as common denominator. Combine all terms into a single fraction with \cos\left(x\right) as common denominator.