Find Trig Functions Using Identities (1+sin(t))/(cos(t))=(cos(t))/(1-sin(t))

$\frac{1 + \sin (t)}{\cos (t)} = \frac{\cos (t)}{1 - \sin (t)}$

To find the value of $\csc (t)$ , use the fact that $\frac{1}{\sin (t)}$ then substitute in the known values.

$\csc (t) = \frac{1}{\sin (t)} = \frac{1}{\frac{\cos (t)}{1 - \sin (t)}}$

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$\csc (t) = \frac{1}{\sin (t)} = 1 (\frac{1 - \sin (t)}{\cos (t)})$

Multiply $\frac{1 - \sin (t)}{\cos (t)}$ by $1$ .

$\csc (t) = \frac{1}{\sin (t)} = \frac{1 - \sin (t)}{\cos (t)}$