Trigonometry Examples

$\frac{\csc^{2} (t) - \cot^{2} (t)}{\sin^{2} (t)}$

Step 1

Apply pythagorean identity.

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

Step 2

Simplify with factoring out.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

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

$\csc^{2} (t)$