## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

We know that $\sin$, $\csc$, and $\tan$ are odd trigonometric functions. This implies that $f(-\theta)=-f(\theta)$ So, $\sin(-\theta)=-\sin(\theta)$ We also know that $\cos$, $\sec$ are even trigonometric functions. This implies that $f(-\theta)=f(\theta)$ So, $\cos(-\theta)=\cos(\theta).$ Thus, $\sin(-\theta)+\cos(-\theta)=-\sin(\theta)+\cos(\theta) =\cos(\theta) -\sin (\theta)$ Therefore, the given statement is True.