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

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

Step 1

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

$\frac{\cos (θ)}{\csc (θ) - 1}$

Step 3

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

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

Step 4

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

$\frac{\cos (θ)}{\csc (θ) - 1}$