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Homework Help: Express tan(2x) in terms of sin(x) alone.

  1. Mar 20, 2008 #1
    1. The problem statement, all variables and given/known data

    Express tan(2x) in terms of sin(x) alone.

    assuming: pi < x < 3pi/2

    2. Relevant equations

    Trig identities

    3. The attempt at a solution

    sin2x/cos2x

    switched for double angle equations;

    (2sinx*cosx)/((cosx)^2 - (sinx)^2)

    then wherever i go with it, it leads nowhere.
     
  2. jcsd
  3. Mar 20, 2008 #2
    [tex]\cos x=\sqrt{1-\sin^2 x}[/tex]

    [tex]\cos{2x}=1-2\sin^2 x[/tex]
     
  4. Sep 25, 2009 #3
    Well tan2x=Sin2x/Cos2x then
    Sin2x= Tan2x*Cos2x but note that Cos^2(2x)=1/Sec^2(2x) using sec^2(2x)=1+ tan^2(2x) we then get
    Sin2x=Tan2x/Sqrt(1+tan^2(2x)) this is all ok but sin2x=2sinxcosx so you need to do the same for cos2x and find cosx in terms of tan2x thus replace it into the expression above.
    I hope this helps.
     
  5. Sep 25, 2009 #4
    Yes I just realised that you can get nicer expression if you see that

    cos2x=1/Sqrt(1+tan^2(2x)) then cos2x=1-2sin^2(x)
    hence
    1-2sin^2(x)=1/(Sqrt(1+tan^2(2x)))
     
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