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Solving Trig equation

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Solve the trig equation exactly in the interval 0≤x≤2π.

tan x + tan π/3
------------------ = square root 3
1 - tan x tan π/3

  • Solving Trig equation - ,

    you should recognize that they are using the formula
    tan(A+B) = (tanA + tanB)/(1 - tanAtanB)

    so
    (tanx + tan π/3)/(1 - tanxtan(π/3) = √3
    becomes
    tan(x+π/3) = √3 ,
    I know tan 60° or tan 240° = √3 OR tan π/3 or tan 4π/3 = √3

    so x+π/3 = π/3 OR x+π/3 = 4π/3
    x = 0 or x = π
    but the period of tanx is π
    so
    x = 0 , π , 2π

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