# Prove trigonometric expression

1. Dec 7, 2011

### sharks

1. The problem statement, all variables and given/known data
Prove that sec^(2)(x/2) divided by 1 - tan^(2)(x/2) is sec x

2. Relevant equations
Trig identities.

3. The attempt at a solution
I used the identity: 1 + tan^2(x) = sec^2(x)

I get for numerator: 1 + tan^2(x/2)
I kept denominator same: 1 - tan^2(x/2)
I get the impression (intuition?) that this can be solved in its current form. But then since i couldn't after a while, i just went on to expand tan^2(x/2) using the double angle formula to get expressions in terms of tan(x). It turned into something lengthy, so i doubt that i'm doing it right.

2. Dec 7, 2011

### Mentallic

You're headed in the wrong direction. Notice that

$$\tan(x)=\frac{\sin(x)}{\cos(x)}$$

and

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

so convert these and simplify, then you can easily apply a double angle formula.

3. Dec 7, 2011

### sharks

OK, got it. Thanks, Mentallic.