Prove trigonometric expression

[DryRun]

Homework Statement

Prove that sec^(2)(x/2) divided by 1 - tan^(2)(x/2) is sec x

Homework Equations

Trig identities.

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.

 

[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.

 

[DryRun]

OK, got it. Thanks, Mentallic.