Consider the following statements

I. If 2 tan^-1 (cos x) = tan^-1 (2 cosec x), then the value of x is \(\frac{\pi}{4}.\)

II. The value of x for which \(\tan^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2}\tan^{-1}x\:\:(x>0)\) is \(\frac{1}{\sqrt3}\).

Which of the above statement(s) is/are correct?