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Math Help - Prove that

  1. #1
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    Question Prove that

    If tanx+tan(x+ pie/3)+tan(x+2pie/3)=3 , then prove that (3tanx -tan^3x)/(1-3tan^2x)=1

    Please show your steps.
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by matsci0000 View Post
    If tanx+tan(x+ pie/3)+tan(x+2pie/3)=3 , then prove that (3tanx -tan^3x)/(1-3tan^2x)=1

    Please show your steps.
    3
    = tanx+tan(x+\frac{\pi}{3})+tan(x+\frac{2\pi}{3})

    = tanx+\frac{tanx+tan\frac{\pi}{3}}{1-tanx.tan\frac{\pi}{3}}+\frac{tanx+tan\frac{2\pi}{3  }}{1-tanx.tan\frac{2\pi}{3}}


    = tanx+\frac{tanx+\frac{\sqrt3}{1}}{1-tanx.\frac{\sqrt3}{1}}+\frac{tanx-\frac{\sqrt3}{1}}{1+tanx.\frac{\sqrt3}{1}}


    = tanx +\frac{8tanx}{1-3tan^2x}

    = \frac{9tanx-3tan^3x}{1-3tan^2x}

    divide both sides of the equation by 3, you get your answer
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