Trigonometry Identities: Simplifying Higher Powers

[NotAMathWhiz]

1. sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?
The possible answers are:
a. 4 sec^2 x
b. 3 sec^2 x - 2
c. sec^2 x + 2
d. tan^2 x - 1

Homework Equations

No idea.

The Attempt at a Solution

I'm not sure where to begin here. My book first doesn't cover anything above squared, and when it does, the equation is by itself and immediately shows an easy way to convert to simpler terms. I'm confused however on how to convert this equation.

does sec^4 x = 1/cos^4 x?

 

[hgfalling]

Yes, sec^4 x is 1/cos^4 x. Try converting everything in the expression to sines and cosines.

 

[NotAMathWhiz]

okay, so is this correct?

1/cos^4 x + 1/cos^2 x * sin^2 x/cos^2 x - 2(sin^4 x/cos^4 x)

 

[Gigasoft]

Yes. Now factorize out $$\frac 1{cos^4x}$$ and factorize the terms containing $$sin^2x$$. Now, you should be able to apply well known identities to get a numerator that only contains terms involving $$cos^2x$$. Now, it should be clear what the answer is.

 

[hgfalling]

Yes, now simplify that.