Precalculus Examples

$\frac{\csc^{2} (x) - \cot^{2} (x)}{\sec (x)} = \cos (x)$

Step 1

Start on the left side.

$\frac{\csc^{2} (x) - \cot^{2} (x)}{\sec (x)}$

Step 2

Apply pythagorean identity.

$\frac{1}{\sec (x)}$

Step 3

Apply the reciprocal identity to $\sec (x)$ .

$\frac{1}{\frac{1}{\cos (x)}}$

Step 4

Simplify.

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Step 4.1

Multiply the numerator by the reciprocal of the denominator.

$1 \cos (x)$

Step 4.2

Multiply $\cos (x)$ by $1$ .

$\cos (x)$

Step 5

Because the two sides have been shown to be equivalent, the equation is an identity.

$\frac{\csc^{2} (x) - \cot^{2} (x)}{\sec (x)} = \cos (x)$ is an identity