#### Answer

The domains for $tan~x$ and $sec~x$ are all the real numbers, except those values of $x$ where $cos~x = 0$. Therefore, the domains of these two functions are the same.
The domains for $cot~x$ and $csc~x$ are all the real numbers, except those values of $x$ where $sin~x = 0$. Therefore, the domains of these two functions are the same.

#### Work Step by Step

$tan~x = \frac{sin~x}{cos~x}$
$sec~x = \frac{1}{cos~x}$
The domains for these two functions are all the real numbers, except those values of $x$ where $cos~x = 0$. Therefore, the domains of these two functions are the same.
We can construct a similar argument for the following two functions:
$cot~x = \frac{cos~x}{sin~x}$
$csc~x = \frac{1}{sin~x}$
The domains for these two functions are all the real numbers, except those values of $x$ where $sin~x = 0$. Therefore, the domains of these two functions are the same.