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Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
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$\frac{\frac{1}{\cos\left(x\right)}-\cos\left(x\right)}{\sec\left(x\right)}$
Learn how to solve problems step by step online. Simplify the trigonometric expression (sec(x)-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. Divide fractions \frac{\frac{1-\cos\left(x\right)^2}{\cos\left(x\right)}}{\sec\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Applying the trigonometric identity: \cos\left(\theta \right)\sec\left(\theta \right) = 1.