Answer
True
Work Step by Step
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.
