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JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Periodic functions

  • question_answer
    The function \[f(x)=\sin \frac{\pi x}{2}+2\cos \frac{\pi x}{3}-\tan \frac{\pi x}{4}\] is period with period  [EAMCET 1992; RPET 2001]

    A) 6

    B) 3

    C) 4

    D) 12

    Correct Answer: D

    Solution :

    Period of \[\sin \frac{\pi x}{2}=\frac{2\pi }{\pi /2}=4\] Period of \[\cos \frac{\pi x}{3}=\frac{2\pi }{\pi /3}=6\] Period of \[\tan \frac{\pi x}{4}=\frac{\pi }{\pi /4}=4\] \[\therefore \]Period of \[f(x)=\]L.C.M. of (4, 6, 4) = 12.


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