JEE Main & Advanced Mathematics Inverse Trigonometric Functions Question Bank Self Evaluation Test - Inverse Trigonometric Functions

  • question_answer
    If \[\sum\limits_{i=1}^{2n}{{{\cos }^{-1}}{{x}_{i}}=0}\] then \[\sum\limits_{i=1}^{2n}{{{x}_{i}}}\]is

    A) n

    B) 2n

    C) \[\frac{n\left( n+1 \right)}{2}\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] Since \[0\le {{\cos }^{-1}}{{x}_{i}}\le \pi ,\therefore {{\cos }^{-1}}{{x}_{i}}=0\] for all i. \[\therefore \]\[{{x}_{i}}=1\] for all \[i\therefore \sum\limits_{i=1}^{2n}{{{x}_{i}}=2n}\]


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