Answer
$\text{True}$
Work Step by Step
Definition of Even and odd functions
If $f(-\theta)=f(\theta)$ then $f$ is an even function
If $f(-\theta)=-f(\theta)$ then $f$ is an odd function.
From the discussions in the book, it has been established that:
$\cos (-\theta)=\cos \theta \quad(\because \text { Even })$
$\sec (-\theta)=\sec \theta \quad(\because \text { even })$
$\sin (-\theta)=-\sin \theta \quad(\because \text { odd })$
$\csc (-\theta)=-\csc \theta \quad(\because odd)$
$\tan (-\theta)=-\tan \theta \quad(\because odd)$
$\cot (-\theta)=-\cot \theta\quad (\because odd)$
Hence cosine and sec are even functions while the rest of the trigonometric functions are odd.
Thus, the given statement is true.
