# How do you simplify #(sec^4x-1)/(sec^4x+sec^2x)#?

##### 1 Answer

Apply a Pythagorean Identity and a couple factoring techniques to simplify the expression to

#### Explanation:

Recall the important Pythagorean Identity

Let's start with the numerator:

Note that this can be rewritten as:

This fits the form of a difference of squares,

From the identity

Let's check out the denominator:

We can factor out a

There isn't much more we can do here, so let's look at what we have now:

We can do some canceling:

Now we rewrite this using only sines and cosines and simplify: