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

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

Apply pythagorean identity.

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

Simplify with factoring out.

Rewrite $1$ as $1^{2}$ .

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

Rewrite $\frac{1^{2}}{\cos^{2} (x)}$ as ${(\frac{1}{\cos (x)})}^{2}$ .

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

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

$\sec^{2} (x)$