Solution for equation

  • #1
How do you find the solution tan(x)=sin(2x)? :confused:
 

Answers and Replies

  • #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.
 
  • #3
No...do i have to do that to find all the solution points?
 
  • #4
robphy
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No...do i have to do that to find all the solution points?
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:
  • #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]
 
  • #6
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square both sides...then make use of (a-b)^2 = (a+b)(a-b)
 
  • #7
robphy
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square both sides...then make use of (a-b)^2 = (a+b)(a-b)
um...
(a-b)^2 = a^2 - 2ab + b^2
a^2 - b^2 = (a+b)(a-b)
 

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