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JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Periodic functions

  • question_answer
    The period of the function \[\sin \left( \frac{\pi x}{2} \right)+\cos \left( \frac{\pi x}{2} \right)\] is  [EAMCET 1990]

    A) 4

    B) 6

    C) 12

    D) 24

    Correct Answer: A

    Solution :

    Period of \[\sin \left( \frac{\pi x}{2} \right)=\frac{2\pi }{\pi /2}=4\] Period of \[\cos \,\left( \frac{\pi x}{2} \right)=\frac{2\pi }{\pi /2}=4\] \[\therefore \] Period of \[\sin \frac{\pi x}{2}+\cos \frac{\pi x}{2}=\]L.C.M. of (4, 4)=4.


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