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Math Help - question about a trig equation

  1. #1
    Junior Member
    Joined
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    question about a trig equation

    could somebody please help me with equation ?
    i think ive just made a stupid mistake because its not working T.T

    Write general solution

    tan2x = cot x

    tan 2x = 2tanx/(1-tansquaredx)

    therefore

    2tanx/(1-tansquaredx) = 1/tanx

    2tansquared x = 1/2

    tan squared x = 1/4

    tan x = + or - 1/2

    which doesnt work
    and the answers say the solution is npi + or - (pi/6)

    thanks for any help !!
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by iiharthero View Post

    2tanx/(1-tansquaredx) = 1/tanx

    2tansquared x = 1/2................WRONG
    \frac{2tanx}{1-tan^2x}=\frac{1}{tanx}

    2tan^2x=1-tan^2x

    tan^2x=\frac{1}{3}
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  3. #3
    Super Member
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    \begin{aligned}<br />
\tan 2x &= \cot x \\<br />
\frac{2\tan x}{1 - \tan^2 x} &= \frac{1}{\tan x} \\<br />
2\tan^2 x &= 1 - \tan^2 x \\<br />
3\tan^2 x &= 1 \\<br />
\tan^2 x &= \frac{1}{3} \\<br />
\tan x &= \frac{\sqrt {3}}{3}<br />
\end{aligned}
    x = \frac{\pi}{6} \pm n\pi


    01


    EDIT: Beaten to it by malaygoel!
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