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Homework Help: Can someone help me w/ these?

  1. Nov 7, 2004 #1
    1)
    tan(x)-sin(x)/2tan(x) = sin^2(x/2)
    1-sin(x)/2 = sin^2(x/2)

    (That's as far as i've gotten on this one...but i don't know if i'm in the right direction or what to do next?)

    2)
    sin2x = 1 / tanx + cot2x
    2sin(x)cos(x) = ''
    sin(x) * cos(x) * sin(x) = ''

    (The same from #1 applies to this problem)
     
  2. jcsd
  3. Nov 7, 2004 #2

    Pyrrhus

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    Homework Helper

    Assuming you mean:
    [tex] \frac{\tan(x)-\sin(x)}{2 \tan(x)} = \sin^{2}(\frac{x}{2}) [/tex]

    Let's change everything to cosinus and sinus

    [tex] \frac{\frac{\sin(x)}{\cos(x)} - \sin(x)}{\frac{2 \sin(x)} {\cos(x)}} = \sin^{2}(\frac{x}{2}) [/tex]

    Simplifying:

    [tex] \frac{\frac{\sin(x) - \sin(x) \cos(x)}{\cos(x)}}{\frac{2 \sin(x)} {\cos(x)}} = \sin^{2}(\frac{x}{2}) [/tex]

    [tex] \frac{\sin(x) - \sin(x) \cos(x)}{2 \sin(x)} = \sin^{2}(\frac{x}{2}) [/tex]

    [tex] \frac{1 - \cos(x)}{2} = \sin^{2}(\frac{x}{2}) [/tex]

    Remember [itex] \sin^{2}(\frac{x}{2}) = \frac{1 - \cos(x)}{2} [/itex]

    [tex] \frac{1 - \cos(x)}{2} = \sin^{2}(\frac{x}{2}) [/tex]

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

    Assuming you mean:
    [tex] \sin (2x) = \frac{1}{\tan(x) + \cot(2x)} [/tex]

    Working the right to the left

    Changing to sinus and cosinus:

    [tex] \sin (2x) = \frac{1}{\frac{\sin(x)}{\cos(x)} + \frac{\cos(2x)}{\sin(2x)}} [/tex]

    Applying double angle identities

    [tex] \sin (2x) = \frac{1}{\frac{\sin(x)}{\cos(x)} + \frac{\cos^2(x) - \sin^2(x)}{2 \sin(x) \cos(x)}} [/tex]

    Simplifying:

    [tex] \sin (2x) = \frac{1}{\frac{2 \sin^2(x) \cos(x) + \cos^3(x) - \sin^2(x) \cos(x)}{2 \sin(x) \cos^2(x)}} [/tex]

    [tex] \sin (2x) = \frac{1}{\frac{\sin^2(x) \cos(x) + \cos^3(x)}{2 \sin(x) \cos^2(x)}} [/tex]

    [tex] \sin (2x) = \frac{1}{\frac{\sin^2(x) + \cos^2(x)}{2 \sin(x) \cos(x)}} [/tex]

    Remember [itex] \sin^2(x) + \cos^2(x) = 1 [/itex]

    [tex] \sin (2x) = \frac{1}{\frac{1}{2 \sin(x) \cos(x)}} [/tex]

    Remember [itex] \sin(2x) = 2 \sin(x) \cos(x) [/itex]

    [tex] \sin (2x) = 2 \sin(x) \cos(x) [/tex]

    [tex] \sin (2x) = \sin (2x) [/tex]
     
    Last edited: Nov 7, 2004
  4. Nov 7, 2004 #3
    damn it... how do u do all these equations on the computer?? i find it hard doin my math on a computer... im more comfortable with a pen and paper... get tired of using the "^",etc

    any words of wisdom ?
     
  5. Nov 7, 2004 #4
    Jeez...that was incredible. Thanks a lot...but I don't suppose there was an easier way, was there? haha
     
  6. Nov 7, 2004 #5

    Pyrrhus

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    Homework Helper

    You get used to imagining it in your head.
     
  7. Nov 7, 2004 #6
    lol i imagine it in my head too when possible but i just cant get myself to type it all down....Good ol' pen and paper!
     
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