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

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

Cancel the common factor of $1 - \csc (θ)$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{\cos (θ)}{1 + \csc (θ)}$ by $1$ .

$\frac{\cos (θ)}{1 + \csc (θ)}$

Rewrite $\csc (θ)$ in terms of sines and cosines.

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

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

$\frac{\cos (θ)}{1 + \csc (θ)}$