JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to \pi /2}{\mathop{\lim }}\,(\sec \theta -\tan \theta )=\] [IIT 1976; AMU 1999]

    A)                 0

    B)                 1/2

    C)                 2

    D)                 \[\infty \]

    Correct Answer: A

    Solution :

                    \[\underset{\theta \to \pi /2}{\mathop{\lim }}\,\,\,\frac{1-\sin \theta }{\cos \theta }=\underset{\theta \to \pi /2}{\mathop{\lim }}\,\,\,\frac{{{\left( \cos \frac{\theta }{2}-\sin \frac{\theta }{2} \right)}^{2}}}{\left( \cos \frac{\theta }{2}-\sin \frac{\theta }{2} \right)\,\left( \cos \frac{\theta }{2}+\sin \frac{\theta }{2} \right)}=0\].


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