Trigonometry Examples

\frac{1 - ({sin}^{2} (x))}{sin (x) - csc (x)}

$\frac{1 - (\sin^{2} (x))}{\sin (x) - \csc (x)}$

Step 1

Apply pythagorean identity.

\frac{{cos}^{2} (x)}{sin (x) - csc (x)}

$\frac{\cos^{2} (x)}{\sin (x) - \csc (x)}$

Step 2

Rewrite

csc (x)

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

\frac{{cos}^{2} (x)}{sin (x) - \frac{1}{sin (x)}}

$\frac{\cos^{2} (x)}{\sin (x) - \frac{1}{\sin (x)}}$

Step 3

Convert from

\frac{1}{sin (x)}

$\frac{1}{\sin (x)}$ to

csc (x)

$\csc (x)$ .

\frac{{cos}^{2} (x)}{sin (x) - csc (x)}

$\frac{\cos^{2} (x)}{\sin (x) - \csc (x)}$