Simplify (cos(theta))/(1-sin(theta))*(1+sin(theta))/(1+sin(theta))

$\frac{\cos (θ)}{1 - \sin (θ)} \cdot \frac{1 + \sin (θ)}{1 + \sin (θ)}$

Cancel the common factor of $1 + \sin (θ)$ .

Cancel the common factor.

$\frac{\cos (θ)}{1 - \sin (θ)} \cdot \frac{1 + \sin (θ)}{1 + \sin (θ)}$

Rewrite the expression.

$\frac{\cos (θ)}{1 - \sin (θ)} \cdot 1$

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

$\frac{\cos (θ)}{1 - \sin (θ)}$