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Math Help - find exact values of Tan 15 degrees and Cos 75 degrees

  1. #1
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    find exact values of Tan 15 degrees and Cos 75 degrees

    Please Help!

    For tan 15 degrees
    Since Tan 45-tan 30=tan 15
    i got this

    1-1/√3 as the exact answer but books answer is (√3-1/√3+1)
    what am i doing wrong?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by jepal View Post
    Since Tan 45-tan 30=tan 15
    Um... not actually. The value of tan(15) is the same as the value of tan(45 - 30), but not at all the same as the value of tan(45) - tan(15)!

    Are you familiar with function notation at all? If so, then note that the tangent function is a function, so "tan(x)" means "f(x)", where the specific name of the function "f" is "tangent". Just as f(a + b) does not mean the same thing as f(a) + f(b), so also tan(45 - 30) does not mean tan(45) - tan(30).

    To simplify tan(45 - 30), you have to use the angle-difference formula they gave you.
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  3. #3
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    Quote Originally Posted by stapel View Post
    Um... not actually. The value of tan(15) is the same as the value of tan(45 - 30), but not at all the same as the value of tan(45) - tan(15)!

    Are you familiar with function notation at all? If so, then note that the tangent function is a function, so "tan(x)" means "f(x)", where the specific name of the function "f" is "tangent". Just as f(a + b) does not mean the same thing as f(a) + f(b), so also tan(45 - 30) does not mean tan(45) - tan(30).

    To simplify tan(45 - 30), you have to use the angle-difference formula they gave you.
    Oh ok! Thank you.
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