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    Maths-
    General
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    Question

    The sum of all the solution of cot invisible function application theta equals sin invisible function application 2 theta comma blank open parentheses theta not equal to n pi comma n blank i n t e g e r close parentheses comma blank 0 less or equal than theta less or equal than pi blankis

    1. 3 pi divided by 2  
    2. pi  
    3. 3 pi divided by 4  
    4. 2 pi  

    The correct answer is: 3 pi divided by 2

      From the given relation
      cos invisible function application theta equals open parentheses 2 sin invisible function application theta cos invisible function application theta close parentheses sin invisible function application theta comma sin invisible function application theta not equal to 0
      rightwards double arrow sin invisible function application theta equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction blank o r cos invisible function application theta equals 0
      rightwards double arrow 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 open parentheses because theta element of open square brackets 0 comma blank pi close square brackets close parentheses
      Then the sum of roots is fraction numerator 3 pi over denominator 2 end fraction

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