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Step-by-step Solution

Problem to solve:

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

Solving method

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

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

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sec(x)-1)/(1-cos(x))=sec(x). 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). Applying the trigonometric identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}.

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

Main topic:

Trigonometric Identities

~ 0.05 s