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

  • question_answer
    If \[{{\tan }^{-1}}\frac{x-1}{x+1}+{{\tan }^{-1}}\frac{2x-1}{2x+1}={{\tan }^{-1}}\frac{23}{36},\]then x =  [ISM Dhanbad 1973]

    A) \[\frac{3}{4},\frac{-3}{8}\]

    B) \[\frac{3}{4},\frac{3}{8}\]

    C) \[\frac{4}{3},\frac{3}{8}\]

    D) None of these

    Correct Answer: D

    Solution :

      \[\frac{x-1}{x+1}+\frac{2x-1}{2x+1}=\frac{23}{36}\left[ 1-\frac{(x-1)(2x-1)}{(x+1)(2x+1)} \right]\] Þ \[24{{x}^{2}}-23x-12=0\Rightarrow (3x-4)(8x+3)=0\]. Hence the result.


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