Simplify (cos(x))/(cos(x)^2)

$\frac{\cos (x)}{\cos^{2} (x)}$

Step 1

Cancel the common factor of $\cos (x)$ and $\cos^{2} (x)$ .

Multiply by $1$ .

$\frac{\cos (x) \cdot 1}{\cos^{2} (x)}$

Cancel the common factors.

Factor $\cos (x)$ out of $\cos^{2} (x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\sec (x)$