Trigonometry Examples

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

Step 1

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

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Step 1.1

Cancel the common factor.

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

Step 1.2

Rewrite the expression.

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

Step 2

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

$\frac{\cos (x)}{1 - \csc (x)}$

Step 3

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

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

Step 4

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

$\frac{\cos (x)}{1 - \csc (x)}$