Question

If ${\displaystyle 3 {\text{sin}}^{-1}\left(\frac{2\text{x}}{1+{\text{x}}^2}\right)-4 {\text{cos}}^{-1}\left(\frac{1-{\text{x}}^2}{1+{\text{x}}^2}\right)+2{\text{tan}}^{-1}\left(\frac{2\text{x}}{1-{\text{x}}^2}\right)=\frac{\pi }{3}}$ then x is equal to ____________.

पर्याय

• ${\displaystyle \frac{1}{\sqrt{3}}}$

• ${\displaystyle \sqrt{3}}$

• 1

• not defined

Answer 1

If ${\displaystyle 3 {\text{sin}}^{-1}\left(\frac{2\text{x}}{1+{\text{x}}^2}\right)-4 {\text{cos}}^{-1}\left(\frac{1-{\text{x}}^2}{1+{\text{x}}^2}\right)+2{\text{tan}}^{-1}\left(\frac{2\text{x}}{1-{\text{x}}^2}\right)=\frac{\pi }{3}}$ then x is equal to ${\displaystyle \underline{\frac{1}{\sqrt{3}}}}$.