Precalculus Examples

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

Step 1

Start on the left side.

$\cos^{2} (θ) - \sin^{2} (θ)$

Step 2

Apply Pythagorean identity in reverse.

$1 - \sin^{2} (θ) - \sin^{2} (θ)$

Step 3

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

$1 - 2 \sin^{2} (θ)$

Step 4

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

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