JEE Main & Advanced Mathematics Inverse Trigonometric Functions Question Bank Inverse trigonometric functions

  • question_answer
    If \[a<\frac{1}{32},\] then the number of solution of \[{{({{\sin }^{-1}}x)}^{3}}+{{({{\cos }^{-1}}x)}^{3}}=a{{\pi }^{3}}\] is

    A) 0

    B) 1

    C) 2

    D) Infinite

    Correct Answer: A

    Solution :

      From previous solution \[\frac{{{\pi }^{3}}}{32}\le {{({{\sin }^{-1}}x)}^{3}}+{{({{\cos }^{-1}}x)}^{3}}\le \frac{7\pi }{8}\] Here\[a<\frac{1}{32}\]. So, number of solution is zero.


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