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Math Help - Finding the Exact value of a tangent using sum and difference

  1. #1
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    Finding the Exact value of a tangent using sum and difference

    I was wondering if someone could check if what i have so far is correct:



    Tan(a - B) =

    tan - 5/12 + tan 7(square root)/3
    -----------------------------------------
    1 - tan -(5/12) (7(square root)/3)


    -5+4 7(square root)
    ------------------------
    12
    -------------------------
    36 + 5 7(square root)
    --------------------------
    36


    Flipping the bottom would get me:

    -5 + 4 7 (squared) (36 - 5 7 (squared))
    ----------------------- ------------------------
    36 + 5 7 (square) (36 - 5 7 (squared))



    I'm not sure if this is correct or not, from looking at my notes the denominator
    is suppose to be a number.

    -180 + 25 7 (squared) + 144 7 (squared) - 20 7 (squared)
    ----------------------------------------------------------------------
    1296 - 180 7 (squared) + 180 7 (squared) - 25 7 (squared)
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  2. #2
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    Quote Originally Posted by MajorJohnson View Post
    I was wondering if someone could check if what i have so far is correct:



    Tan(a - B) =

    tan - 5/12 + tan 7(square root)/3
    -----------------------------------------
    1 - tan -(5/12) (7(square root)/3)


    -5+4 7(square root)
    ------------------------
    12
    -------------------------
    36 + 5 7(square root)
    --------------------------
    36


    Flipping the bottom would get me:

    -5 + 4 7 (squared) (36 - 5 7 (squared))
    ----------------------- ------------------------
    36 + 5 7 (square) (36 - 5 7 (squared))



    I'm not sure if this is correct or not, from looking at my notes the denominator
    is suppose to be a number.

    -180 + 25 7 (squared) + 144 7 (squared) - 20 7 (squared)
    ----------------------------------------------------------------------
    1296 - 180 7 (squared) + 180 7 (squared) - 25 7 (squared)
    This looks somewhat garbled. I'm assuming that tan(A) = 5/12 and tan(B) = √7/3. The formula for tan(AB) is (tan(A) tan(B))/(1 + tan(A)tan(B)). So the fraction should be
    ....5/12 √7/3.... .
    1 + (5/12)(√7/3)

    Multiply top and bottom by 36, to get
    15 12√7 .
    ..36 5√7

    Next, multiply top and bottom by 36 + 5√7, so that the denominator becomes an integer.
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