Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

Apply pythagorean identity.

$\sec (x) \cos^{2} (x)$

Step 3

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

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

Step 4

Cancel the common factor of $\cos (x)$ .

$\cos (x)$

Step 5

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

$\sec (x) (1 - \sin^{2} (x)) = \cos (x)$ is an identity