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If t a n x+tan(x+pi/3)+tan(x+(2pi)/3)=3,...

If `t a n x+tan(x+pi/3)+tan(x+(2pi)/3)=3,` then prove that `(3tanx-t a n^3x)/(1-3t a n^2x)=1` .

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To solve the problem, we start with the equation given: \[ \tan x + \tan\left(x + \frac{\pi}{3}\right) + \tan\left(x + \frac{2\pi}{3}\right) = 3 \] ### Step 1: Use the tangent addition formula We will use the tangent addition formula: ...
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Knowledge Check

  • If tanx+tan((pi)/3+x)+tan((2pi)/3+x)=3 ,then

    A
    tanx=1
    B
    tan2x=1
    C
    tan3x=1
    D
    None of these

  • If tanx+tan((pi)/(3)-x)+tan((2pi)/(3)+x)=3 , then

    A
    tan x =1
    B
    tan 2x =1
    C
    tan 3x = 1
    D
    None of these

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