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Math Help - Trigonometric equation

  1. #1
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    Trigonometric equation

    how can i solve this equation 2cot^2(2x)+3cosec2x=0 for o<x<π??
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  2. #2
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    Re: Trigonometric equation

    Endri
    Substitute cot(2x) by cosx/sinx and cosec2x by 1/sin2x and do some work to get a quadratic then solve it it is easy.
    good luck
    Last edited by MINOANMAN; February 21st 2013 at 08:42 AM.
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  3. #3
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    Re: Trigonometric equation

    Hello, endri!

    \text{Solve: }\:2\cot^2(2x)+3\csc(2x)\:=\:0\,\text{ for }0 < x < \pi.

    We have: . 2\cot^2(2x) + 3\csc(2x) \:=\:0

    . . . . 2[\csc^2(2x) - 1] + 3\csc(2x) \:=\:0

    . . . . . 2\csc^2(2x) - 2 + 3\csc(2x) \:=\:0

    . . . . . 2\csc^2(2x) + 3\csc(2x) - 2 \:=\:0

    . . . . [2\csc(2x) - 1][\csc(2x)+2] \:=\:0


    Then: . \begin{Bmatrix}2\csc(2x) - 1 \:=\:0 & \Rightarrow & \csc(2x) \:=\:\frac{1}{2} && \text{No real roots} \\ \csc(2x) + 2\:=\:0 & \Rightarrow & \csc(2x) \:=\:-2 & \Rightarrow & 2x \:=\:\frac{7\pi}{6},\,\frac{11\pi}{6} & \Rightarrow & \boxed{x \:=\:\tfrac{7\pi}{12},\,\tfrac{11\pi}{12}} \end{Bmatrix}
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  4. #4
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    Re: Trigonometric equation

    I strongly believe that we should guide the readers to do some work by themselves and study more rather than solve them their homework.

    MINOAS
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  5. #5
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    Re: Trigonometric equation

    THANK YOU VERY MUCH MAN
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  6. #6
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    Re: Trigonometric equation

    cosec^2(x)=1+cot^2(x),,and i wasnt sure if it was right to say that cosec^2(2x)=1+cot^2(2x)... thanks again man
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  7. #7
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    Re: Trigonometric equation

    minoanaman thanks for your help too man.. i had solved this equation,but i was not sure if the method that soroban showed me was right
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