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

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

Apply pythagorean identity.

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

Simplify with factoring out.

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

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

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

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

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

$\sec^{2} (t)$