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    Maths-
    General
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    Question

    The set of values of theta satisfying the inequation 2 sin to the power of 2 end exponent invisible function application theta minus 5 sin invisible function application theta plus 2 greater than 0, where 0 less than theta less than 2 pi, is

    1. open parentheses 0 comma blank fraction numerator pi over denominator 6 end fraction close parentheses union open parentheses fraction numerator 5 pi over denominator 6 end fraction comma blank 2 pi close parentheses  
    2. open square brackets 0 comma blank fraction numerator pi over denominator 6 end fraction close square brackets union open square brackets fraction numerator 5 pi over denominator 6 end fraction comma blank 2 pi close square brackets  
    3. open square brackets 0 comma blank fraction numerator pi over denominator 3 end fraction close square brackets union open square brackets fraction numerator 2 pi over denominator 3 end fraction comma blank 2 pi close square brackets  
    4. None of these  

    The correct answer is: open parentheses 0 comma blank fraction numerator pi over denominator 6 end fraction close parentheses union open parentheses fraction numerator 5 pi over denominator 6 end fraction comma blank 2 pi close parentheses

      Given, 2 sin to the power of 2 end exponent invisible function application theta minus 5 sin invisible function application theta plus 2 greater than 0
      rightwards double arrow blank open parentheses 2 sin invisible function application theta minus 1 close parentheses open parentheses sin invisible function application theta minus 2 close parentheses greater than 0

      open parentheses 2 sin invisible function application theta minus 1 close parentheses less than 0 blank rightwards double arrow blank sin invisible function application theta less than fraction numerator 1 over denominator 2 end fraction
      It is clear from the figure
      theta element of open parentheses 0 comma fraction numerator pi over denominator 6 end fraction close parentheses union open parentheses fraction numerator 5 pi over denominator 6 end fraction comma blank 2 pi close parentheses

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