Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

Apply Pythagorean identity in reverse.

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

Step 3

Add $1$ and $1$ .

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

Step 4

Reorder terms.

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

Step 5

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

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