Question

How do you simply sec(-x)?

Answer 1

`sec(-x)=1/cos(x)=sec(x)`

Explanation:

You probably meant "simplify".
The secant function is only the inverse of the cosine function.
So `sec (x) = 1/cos(x)`.

Now, the cosine function is said to be an "even" function.
That is, if you put `-x` instead of `x`, you still get the same thing.
So, `cos (-x) = cos(x)`

Therefore,
`sec(-x)=1/cos(-x)=1/cos(x)=sec(x)`

I hope this helps!

Answer 2

Since secant is an even function f(-x)= f(x), so therefore to simplify it, it's just sec(x)

Explanation:

Sec and Cos are even functions, meaning they have y-axis symmetry
Tan, Cot, Sin, Csc are odd functions, meaning that they have origin symmetry and f(-x) in this case is equal to -f(x).