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Thread: question about a trig equation

  1. #1
    Junior Member
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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
    $\displaystyle \frac{2tanx}{1-tan^2x}=\frac{1}{tanx}$

    $\displaystyle 2tan^2x=1-tan^2x$

    $\displaystyle tan^2x=\frac{1}{3}$
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  3. #3
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    $\displaystyle \begin{aligned}
    \tan 2x &= \cot x \\
    \frac{2\tan x}{1 - \tan^2 x} &= \frac{1}{\tan x} \\
    2\tan^2 x &= 1 - \tan^2 x \\
    3\tan^2 x &= 1 \\
    \tan^2 x &= \frac{1}{3} \\
    \tan x &= \frac{\sqrt {3}}{3}
    \end{aligned}$
    $\displaystyle x = \frac{\pi}{6} \pm n\pi$


    01


    EDIT: Beaten to it by malaygoel!
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