A) 3
B) \[-\sqrt{3}\]
C) \[\sqrt{2}\]
D) \[2\]
E) \[\sqrt{3}\]
Correct Answer: E
Solution :
Given, \[5{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)+7{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\] \[-4{{\tan }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)-{{\tan }^{-1}}x=5\pi \] \[\therefore \] \[5(2{{\tan }^{-1}}x)+7(2{{\tan }^{-1}}x)\] \[-4(2{{\tan }^{-1}}x)-{{\tan }^{-1}}x=5\pi \] \[\Rightarrow \] \[15{{\tan }^{-1}}x=5\pi \] \[\Rightarrow \] \[{{\tan }^{-1}}x=\frac{\pi }{3}\] \[\Rightarrow \] \[x=\sqrt{3}\]You need to login to perform this action.
You will be redirected in
3 sec