#### Answer

False

#### Work Step by Step

RECALL:
(1) $\csc{\theta} = \frac{r}{y}$
(2) $\sec{\theta} = \frac{r}{x}$
Since they have the different denominators, then the values for which they are not defined must be different.
Example:
Cosecant is not defined when $x=0$, but secant is defined when $x=0$.
Secant is not defined when $x=\frac{\pi}{2}$ but cosecant is defined when $x=\frac{\pi}{2}$.