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Need help with a problem (sum of two angles)

  1. Oct 15, 2014 #1
    1. The problem statement, all variables and given/known data

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


    3. 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?.
     
  2. jcsd
  3. Oct 15, 2014 #2

    Mark44

    Staff: Mentor

    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,
     
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