Trigonometry Examples

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

Step 1

Start on the right side.

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

Step 2

Apply Pythagorean identity in reverse.

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

Step 3

Subtract ${\sin (a)}^{2}$ from $- {\sin (a)}^{2}$ .

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

Step 4

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

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