# How do you change sec^3(x) - sec(x) into an expression with only sines and cosines?

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Use fundamental identities to change the expression sec^3(x) - sec(x) to one involving only sines and cosines. Then simplify.

I am at a complete loss on how I can do this. I have spent an hour looking up fundamental identities and derivatives and I still can't make any progress on this problem at all.

Use fundamental identities to change the expression sec^3(x) - sec(x) to one involving only sines and cosines. Then simplify.

I am at a complete loss on how I can do this. I have spent an hour looking up fundamental identities and derivatives and I still can't make any progress on this problem at all.

##### 1 Answer

Use

#### Explanation:

Formatted problem:

Remember that

First, we can use the distributive property to take out a

Here, we consider the Pythagorean Identity

which is equal to

by subtracting

Continuing on, we see that we can substitute

Now, since we know that

By simplifying, we get our final answer as:

Hope this helps.