Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

Apply the reciprocal identity to $\csc (x)$ .

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

Step 3

Simplify each term.

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

Step 4

Now consider the right side of the equation.

$\csc (x) - \sin (x)$

Step 5

Apply the reciprocal identity to $\csc (x)$ .

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

Step 6

Because the two sides have been shown to be equivalent, the equation is an identity.

$\frac{1}{\sin (x)} - \frac{1}{\csc (x)} = \csc (x) - \sin (x)$ is an identity