How do you simply sec(-x)?

Feb 18, 2018

$\sec \left(- x\right) = \frac{1}{\cos} \left(x\right) = \sec \left(x\right)$

Explanation:

You probably meant "simplify".
The secant function is only the inverse of the cosine function.
So $\sec \left(x\right) = \frac{1}{\cos} \left(x\right)$.

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, $\cos \left(- x\right) = \cos \left(x\right)$

Therefore,
$\sec \left(- x\right) = \frac{1}{\cos} \left(- x\right) = \frac{1}{\cos} \left(x\right) = \sec \left(x\right)$

I hope this helps!

Feb 18, 2018

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).