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Math Help - Help Needed with this Trig Equation!

  1. #1
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    Help Needed with this Trig Equation!

    Hi, could someone show me how this one's done?

    Find all solutions for X, satisfying 0 < X < (two pi):
    2cotX = tanX

    Thanks, your help would be much appreciated!
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  2. #2
    MHF Contributor chisigma's Avatar
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    Supposing that \tan x \ne 0 You can devide both terms by \tan x and after some steps You arrive at the equation \tan x = \pm \sqrt{2} which has four solutions, one for each quadrant...

    Kind regards

    \chi \sigma
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  3. #3
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    Thanks very much!
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  4. #4
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    Quote Originally Posted by sammysparrow View Post
    Hi, could someone show me how this one's done?

    Find all solutions for X, satisfying 0 < X < (two pi):
    2cotX = tanX

    Thanks, your help would be much appreciated!
    2cotx-tanx=0

    \displaystyle\frac{2}{tanx}-tanx=0\Rightarrow\frac{2tanx}{tanx}-tan^2x=tanx(0)=0

    2-tan^2x=0\Rightarrow\ (\sqrt{2}+tanx)(\sqrt{2}-tanx=0)

    tanx gives the slope of a line passing through the origin with an angle x,

    hence the one with positive slope traverses quadrants 1 and 3,
    while the other traverses quadrants 2 and 4.

    x=tan^{-1}\sqrt{2},\;\;{\pi}+tan^{-1}\sqrt{2},\;\;2{\pi}-tan^{-1}\sqrt{2},\;\;{\pi}-tan^{-1}\sqrt{2}
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  5. #5
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    Thanks very much, that's very helpful.
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