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Question

The sum of all the solution of cotθ= sin 2θ(θ ≠ nstraight pi, n integer), 0 ,less or equal than theta less or equal than pi is

  1. 3straight pi/2    
  2. straight pi
  3. infinite    
  4. 2straight pi
       

The correct answer is: 3straight pi/2


    For the given relation cos q = (2 sin q cos q) sin q, sin q¹ 0
    table row cell text end text text o end text text r end text text end text s i n invisible function application theta equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction text end text text o end text text r end text text end text c o s invisible function application theta equals 0 end cell row cell text end text text o end text text r end text text end text theta equals fraction numerator pi over denominator 4 end fraction comma fraction numerator 3 pi over denominator 4 end fraction comma fraction numerator pi over denominator 2 end fraction end cell end table
    Then the sum of roots is 3p/2

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