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

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

Apply pythagorean identity.

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

Simplify with factoring out.

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

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

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

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

Convert from $\frac{1}{\sin (t)}$ to $\csc (t)$ .

$\csc^{2} (t)$