A) \[\frac{1}{\sqrt{3}}\]
B) \[-\frac{1}{\sqrt{3}}\]
C) \[\sqrt{3}\]
D) \[-\frac{\sqrt{3}}{2}\]
E) \[\frac{\sqrt{3}}{2}\]
Correct Answer: A
Solution :
We have, \[3{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)-4{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)\] \[+2{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)=\frac{\pi }{3}\] \[\Rightarrow \]\[6{{\tan }^{-1}}x-8{{\tan }^{-1}}x+4{{\tan }^{-1}}x=\frac{\pi }{3}\] \[\Rightarrow \] \[2{{\tan }^{-1}}x=\frac{\pi }{3}\] \[\Rightarrow \] \[{{\tan }^{-1}}x=\frac{\pi }{6}\] \[\Rightarrow \] \[x=\tan \frac{\pi }{6}=\frac{1}{\sqrt{3}}\]
You need to login to perform this action.
You will be redirected in
3 sec
