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Trigonometry and Identities

  1. May 1, 2016 #1
    1. The problem statement, all variables and given/known data
    sin^2x + 4sinx +4 / sinx + 2 = sinx +2

    2. Relevant equations


    3. The attempt at a solution
    L.S = sin^2x + 4sinx +4 / sinx + 2
    =1-cos^2+4(sinx + 1) / sinx +2

    Not sure where to go from there.
    Not sure if I was even supposed to factor out the 4?
     
  2. jcsd
  3. May 1, 2016 #2

    SammyS

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    Please enclose the entirety of any numerator and/or denominator in parentheses.
     
  4. May 1, 2016 #3
    (Sin^2x + 4sinx + 4) / (sinx + 2) = sinx + 2
     
  5. May 1, 2016 #4

    SammyS

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    Factor the numerator.
     
  6. May 1, 2016 #5
    Thank you, didn't catch that.
     
  7. May 1, 2016 #6

    SammyS

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    So, what do you get ?
     
  8. May 1, 2016 #7
    ((Sinx + 2)(Sinx + 2)) / (Sinx + 2)

    Then you cancel one from top and bottom to get: Sinx + 2.
     
  9. May 1, 2016 #8

    micromass

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    Yes, but it is a tiny bit more complicated. Here's something to think about:

    1) Why doesn't the following equality hold for all ##x##:

    [tex]\frac{(x+2)(x+2)}{x+2} = x+2[/tex]

    2) Why is this no problem with the question in the OP?
     
  10. May 1, 2016 #9
    ((Sinx + 2)(Sinx + 2)) you then take reciprocal of denominator and multiply it by the numerator, and that it is when you cancel them out?
     
  11. May 2, 2016 #10

    Math_QED

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    Can you always divide out common factors from numerator and denumerator? For example, can you always say that (cosx-1)(cosx + 1)/(cosx - 1) = cosx + 1?

    Why can/can't you say that? And what about your expression, those are things you have to think about!
     
  12. May 3, 2016 #11
    To give you a hint, what happens if we plug in -2 for x? Pay attention to the denominator.
     
  13. May 3, 2016 #12

    Mark44

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    micromass asked two questions. You didn't respond to his first question, and your answer to the second question doesn't address why ##\frac{(\sin x+2)(\sin x+2)}{\sin x+2} = \sin x+2## is always true, regardless of the value of x.
     
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