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The general solution of the trigonometric equation tan x + tan 2x + tan 3x = tan x · tan 2x tan 3x is
where n element of I

  1. x = nstraight pi  
  2. n pi plus-or-minus fraction numerator pi over denominator 3 end fraction    
  3. x = 2nstraight pi    
  4. x equals fraction numerator n pi over denominator 3 end fraction    

The correct answer is: x equals fraction numerator n pi over denominator 3 end fraction


    We know that
    tan x · tan 2x · tan 3x = tan 3x – tan 2x – tan x
    hence tan x + tan 2x + tan 3x = tan 3x – tan 2x – tan x
    Þ tan x + tan 2x = 0
    \ tan 2x = tan (– x)
    2x = np – x
    x equals fraction numerator n pi over denominator 3 end fraction comma n element of I

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