** Final Answer

**

** Step-by-step Solution **

Problem to solve:

** Specify the solving method

**

**

Starting from the left-hand side (LHS) of the identity

Learn how to solve differential calculus problems step by step online.

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

Learn how to solve differential calculus problems step by step online. Prove the trigonometric identity (sec(x)-1)/(1-cos(x))=sec(x). Starting from the left-hand side (LHS) of the identity. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Combine all terms into a single fraction with \cos\left(x\right) as common denominator. Simplify the fraction \frac{\frac{1-\cos\left(x\right)}{\cos\left(x\right)}}{1-\cos\left(x\right)} by 1-\cos\left(x\right).

** Final Answer

**