2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Inverse Trigonometric Functions

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

  • question_answer
    If \[3{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)-4{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)+2{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)=\frac{\pi }{3}\]where \[\left| x \right|<1,\]then x is equal to

    A) \[\frac{1}{\sqrt{3}}\]                 

    B) \[-\frac{1}{\sqrt{3}}\]

    C) \[\sqrt{3}\]                    

    D) \[-\frac{\sqrt{3}}{4}\]

    Correct Answer: A

    Solution :

    [a] The given equation is \[3(2ta{{n}^{-1}}x)-4(2ta{{n}^{-1}}x)+2(ta{{n}^{-1}}x)=\pi /3\] \[\therefore 2{{\tan }^{-1}}x=\pi /3\] \[\therefore {{\tan }^{-1}}x=\pi /6\] \[\therefore x=\frac{1}{\sqrt{3}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner