JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    For \[\theta >\frac{\pi }{3}\], the value of \[f(\theta )={{\sec }^{2}}\theta +{{\cos }^{2}}\theta \] always lies in the interval [Orissa JEE 2002]

    A)                    (0, 2)

    B)            [0, 1]

    C)            (1, 2)

    D)            \[[2,\ \infty )\]

    Correct Answer: D

    Solution :

               \[-1\le \cos \theta \le 1\] Þ \[=-\frac{1}{{{a}^{2}}}\]            and \[{{\sec }^{2}}\theta \ge 1\]for \[\theta >\frac{\pi }{3}\] , \[\sec \theta \ge 2\]            Þ \[{{\sec }^{2}}\theta \ge 4\].  \ Required interval \[=[2,\,\,\infty )\].


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