Final answer to the problem
Step-by-step Solution
Specify the solving method
Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
Learn how to solve simplify trigonometric expressions problems step by step online.
$\frac{\frac{1}{\cos\left(x\right)^2}-1}{\sec\left(x\right)^2}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (sec(x)^2-1)/(sec(x)^2). 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)^2 as common denominator. Divide fractions \frac{\frac{1-\cos\left(x\right)^2}{\cos\left(x\right)^2}}{\sec\left(x\right)^2} 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)\cdot\sec\left(\theta\right)=1.