Need help with a problem (sum of two angles)

[Charlie Prieto]

Homework Statement

Hello, all. This here's the problem: Use the difference formula to solve for the exact value of tan(15°).

Homework Equations

The Attempt at a Solution

I've solved it up until this point:
I used the formula to get (tan(45°)-tan(30°)) / (1 + tan(45°)tan(30°)).
(1 - (sqrt(3)/3)) / (1 + (1)(sqrt(3)/3)). How do I get 2 - sqrt(3), which I know is the answer, from the point I'm at?.

 

[Mark44]

Homework Statement

Hello, all. This here's the problem: Use the difference formula to solve for the exact value of tan(15°).

Homework Equations

The Attempt at a Solution

I've solved it up until this point:
I used the formula to get (tan(45°)-tan(30°)) / (1 + tan(45°)tan(30°)).
(1 - (sqrt(3)/3)) / (1 + (1)(sqrt(3)/3)). How do I get 2 - sqrt(3), which I know is the answer, from the point I'm at?.

In the numerator, combine the fractions 1/1 and -√3/3. Do the same in the denominator, which is only slightly different. At this point, you'll have what is called a complex fraction, one in which both the numerator and denominator are themselves fractions.

To simplify a complex fraction that looks like this...
$$\frac{ \frac{a + b}{c} }{\frac{ e + f}{c}}$$
multiply by 1 in the form of c/c.

Finally, you'll need to rationalize the denominator,