Determine if True sin(-theta)+cos(-theta)=cos(theta)-sin(theta)

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

Step 1

Start on the left side.

$\sin (- θ) + \cos (- θ)$

Step 2

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

$- \sin (θ) + \cos (- θ)$

Step 3

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

$- \sin (θ) + \cos (θ)$

Step 4

Reorder terms.

$\cos (θ) - \sin (θ)$

Step 5

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

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