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Homework Help: Trigonometry (identitites)

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Let A,B,C be three angles such that A=45 (degrees) and tanBtanC=p. Find all possible values of p such that A,B,C are the angles of a triangle.


    2. Relevant equations



    3. The attempt at a solution

    I got an expression for cos(B-C)= (1+p)/{(p-1)√2}
    My book says this-
    Since B or C can vary from 0 to 135,
    -1/√2 < (1+p)/{(p-1)√2} <= 1

    I did not understand how this step came. Please help
     
  2. jcsd
  3. Sep 11, 2010 #2

    vela

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    Hint: You know that B+C=135, so B=135-C and B-C=135-2C.
     
  4. Sep 11, 2010 #3
    But B-C=135-2C is not independent of C.
    How will that help?
     
  5. Sep 11, 2010 #4

    vela

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    Why should it be independent of C? Think about what range of values C can assume and what this means about range of values cos(B-C) can assume.
     
  6. Sep 11, 2010 #5
    Thanks, I got it
     
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