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Another trigonometry problem

  1. Apr 10, 2007 #1
    in part b) i of a question, i was asked to prove that (1-cos2x)/sin2x is equivilent to tanx and so i did.

    then in part b) ii i was asked to varify that 180 is a solution of x for:
    sin2x = 2 - 2cos2x

    i took the 2 out; sin2x = 2(1 - cos2x) and saw similarities to part i,
    so i divided by 2sin2x to get
    (1-cos2x)/sin2x = 1/2
    which using part i i deduced that tanx = 1/2

    but 180 isnt the solution of this. (26.6 is)

    where did I go wrong, was it because I divided through by a the 2sin2x when i shouldn't have?
    in my other trig question thread it was apparently ok to divide by a trig funtion, if this is the problem here why does it apply to this and not my other question

    NB part a of the question seems irrelevant.
    part b) iii however asks me to find the other 2 solutions, of which 26.6 is one of the answers
    so how do i get to 180 and the other solution for part b) iii
  2. jcsd
  3. Apr 10, 2007 #2


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    It's ok to divide by a trig function unless in the end that trig function turns out to be zero. If you put 180 in sin(2x) you get zero. So the original equation has zeros that the divided equation does not. Eg. x*(x-1)=0 has the solutions 0,1. (x-1)=0 has only 1.
  4. Apr 10, 2007 #3
    ok so as sin2x = 0 for x=180, when you divide it goes.

    so if i cant do that then how do i varify that x=180

    i've already found out how to get the other solution, i forgot to mention that the interval is (0, 360)
  5. Apr 10, 2007 #4


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    When you divide by something make a note to yourself to check in the end that the thing you divided by is not zero, and if it is zero, then check that it is not an extra root. So you need to solve both tan(x)=1/2 and sin(2x)=0 and then check if all such values are really roots. Ie substitute them into sin2x = 2 - 2cos2x.
  6. Apr 10, 2007 #5
    To verify x=180 is a solution
    LHS is sin(360)=0
    RHS is 2 -2cos(360)=2-2=0
    LHS=RHS so x=180 is a solution

    to obtain x=180 as a solution



    sin2x=0 or 1-2tanx=0
  7. Apr 10, 2007 #6
    ahh its all clear now, would either one of the above proofs for x=180 be valid as an answer or will the latter have to be shown?
  8. Apr 10, 2007 #7
    Depends on the wording of the question

    verify that x=180 is a solution of ..... use the first method

    show that x=180 is a solution of...... use the second method.
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