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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2011

  • question_answer
    The number of roots of the equation \[x+2\text{ }\tan x=\pi /2\]in the interval\[[0,2\pi ]\]is

    A)  1               

    B)  2

    C)  3               

    D)  infinite

    Correct Answer: C

    Solution :

     We have, \[x+2\tan x=\pi /2\] \[\Rightarrow \] \[\tan x=\pi /4-x/2\] Let\[y=tan\text{ }x\]and \[y=\pi /4-x/2\] The curves\[y=tan\text{ }x\]and \[y=\pi /4-x/2\] in the interval\[[0,2\pi ],\]intersect at three points. The abscissa of these three points are the roots of the equation.


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