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Starting from the left-hand side (LHS) of the identity
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$\frac{\sec\left(x\right)-1}{1-\cos\left(x\right)}$
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).