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

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true

##  Step-by-step Solution 

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

$\frac{\sec\left(x\right)-1}{1-\cos\left(x\right)}$
2

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

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

Learn how to solve trigonometric identities problems step by step online.

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

Learn how to solve trigonometric identities 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).

true

##  Explore different ways to solve this problem

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Prove from RHS (right-hand side)Express everything into Sine and Cosine

### Main Topic: Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.