Question

How do you find the exact expression of `cos (pi / 2) - sec (-pi/2)`?

Answer 1

You can't write that expression because it would lead to a division by zero.

Explanation:

First of all, use the fact that, by definition, `sec(x)=1/cos(x)`.

So, your expression becomes

`cos(pi/2) - 1/cos(-pi/2)`

Now you can use the fact that `cos(-x)=cos(x)`, and it becomes

`cos(pi/2) - 1/cos(pi/2)`

Now, the problem is that `cos(pi/2)=0`, and so the first term is zero, but the second would be something like `1/0` which is obviously impossible to write. So, your expression can't be evaluated in that point, because `-pi/2` is out of the domain of `sec(x)`.