Trigonometry Examples

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

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

Step 1

Start on the left side.

cos (- x) - sin (- x)

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

Step 2

Since

cos (- x)

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

cos (- x)

$\cos (- x)$ as

cos (x)

$\cos (x)$ .

cos (x) - sin (- x)

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

Step 3

Since

sin (- x)

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

sin (- x)

$\sin (- x)$ as

- sin (x)

$- \sin (x)$ .

cos (x) - - sin (x)

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

Step 4

Multiply

- - sin (x)

$- - \sin (x)$ .

cos (x) + 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)

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