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Math Help - trigonometric problem

  1. #1
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    trigonometric problem

    Given tan\frac{A}{2}=\frac{1}{2},find the value of cot A
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  2. #2
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    hELLO, mastermin346!

    We need two identities:

    . . \tan2\theta \:=\:\dfrac{2\tan\theta}{1 - \tan^2\!\theta}

    . . \cot\theta \:=\:\dfrac{1}{\tan\theta}



    Given: \tan\frac{A}{2}=\frac{1}{2}, find the value of \cot A

    \tan A \;=\;\dfrac{2\tan\frac{A}{2}}{1-\tan^2\!\frac{A}{2}} \;=\;\dfrac{2(\frac{1}{2})}{1 - (\frac{1}{2})^2} \;=\;\dfrac{1}{\frac{3}{4}} \;=\;\dfrac{4}{3}


    Therefore: . \cot A \;=\;\dfrac{1}{\frac{4}{3}} \;=\;\dfrac{3}{4}

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  3. #3
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    tan A= tan(2*A/2)=2tan(A/2)/[1-tan^2(A/2)]=4/3.
    cot A=1/tan A=3/4.
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