Trigonometry Examples

$\cos (- x) - \sin (- x) = \cos (x) + \sin (x)$

Step 1

Start on the left side.

$\cos (- x) - \sin (- x)$

Step 2

Since $\cos (- x)$ is an even function, rewrite $\cos (- x)$ as $\cos (x)$ .

$\cos (x) - \sin (- x)$

Step 3

Since $\sin (- x)$ is an odd function, rewrite $\sin (- x)$ as $- \sin (x)$ .

$\cos (x) - - \sin (x)$

Step 4

Multiply $- - \sin (x)$ .

$\cos (x) + \sin (x)$

Step 5

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

$\cos (- x) - \sin (- x) = \cos (x) + \sin (x)$ is an identity