Trigonometry Examples

$\csc^{2} (x) \cdot \sin (x) = \frac{\sec^{2} (x) - \tan^{2} (x)}{\sin (x)}$

Step 1

Start on the right side.

$\frac{\sec^{2} (x) - \tan^{2} (x)}{\sin (x)}$

Step 2

Apply pythagorean identity.

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

Step 3

Rewrite $\frac{1}{\sin (x)}$ as $\csc^{2} (x) \cdot \sin (x)$ .

$\csc^{2} (x) \cdot \sin (x)$

Step 4

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

$\csc^{2} (x) \cdot \sin (x) = \frac{\sec^{2} (x) - \tan^{2} (x)}{\sin (x)}$ is an identity