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Homework Help: Trignometric Identities

  1. Sep 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that
    [tex]\frac{sin3x}{sinx}[/tex]-[tex]\frac{cos3x}{cosx}[/tex] = 2

    2. Relevant equations

    3. The attempt at a solution

    =[tex]\frac{sin2x.cosx + cos2x.sinx}{sin}-\frac{cos2xcosx - sin2x.sinx}{cosx}[/tex]
  2. jcsd
  3. Sep 7, 2009 #2
    thats as far i got...im really new with trig ..caught a wake up call at school so i started working with it...
  4. Sep 7, 2009 #3
    By multiplying [itex]\frac{sin3x}{sinx}[/itex] with [itex]\frac{cos(x)}{cos(x)}[/itex] and [itex]\frac{cos(3x)}{cos(x)}[/itex] with [itex]\frac{sin(x)}{sin(x)}[/itex] you got:


    What can you spot now? :smile:
  5. Sep 7, 2009 #4
    Did you try getting a common denominator at this point?
  6. Sep 8, 2009 #5
    can we expand sin(3x) and cos(3x) using double angle formula?
  7. Sep 8, 2009 #6
    It can also be done onwards from here. Do you know how to expand cos(2x) and sin(2x)?
  8. Sep 8, 2009 #7

    You can write the nominator:




    using the sum difference formula.

    Also you can write the denominator




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