Trigonometry Examples

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

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

Step 1

Start on the left side.

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

Step 2

Apply Pythagorean identity in reverse.

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

Step 3

Subtract

${\sin (x)}^{2}$ from

$- {\sin (x)}^{2}$ .

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

Step 4

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

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