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Solution for equation

  1. Apr 4, 2007 #1
    How do you find the solution tan(x)=sin(2x)? :confused:
     
  2. jcsd
  3. Apr 4, 2007 #2

    cristo

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    Can you express both sides in terms of sin(x) and cos(x)? That might be a good place to start.
     
  4. Apr 4, 2007 #3
    No...do i have to do that to find all the solution points?
     
  5. Apr 4, 2007 #4

    robphy

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    You could plot them and look for the intersection points.
    But cristo's suggestion would probably yield more accurate ["closed form"] answers. (Be careful not to inadvertently throw away solutions.)
     
    Last edited: Apr 4, 2007
  6. Apr 4, 2007 #5

    danago

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    You can easily do it using the fact that:

    [tex]
    \begin{array}{l}
    \tan x \equiv \frac{{\sin x}}{{\cos x}} \\
    \sin (2x) \equiv 2\sin x\cos x \\
    \end{array}
    [/tex]
     
  7. Apr 5, 2007 #6
    square both sides...then make use of (a-b)^2 = (a+b)(a-b)
     
  8. Apr 5, 2007 #7

    robphy

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    um...
    (a-b)^2 = a^2 - 2ab + b^2
    a^2 - b^2 = (a+b)(a-b)
     
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