Statement I : `y= -tan^(-1)(x^(-1))+1` is an increasing function of x
Statement II : `(dy)/(dx)` is positive for all values of x which one of the following is correct in respect of the above statements?

Options

A. Both statement I and II are independently correct and statement II is the correct explanation of statementI
B. Both I and II are independently correct but statement II is not the correct explanation of statement I
C. Statement I is correct but statement I is false
D. Statement I is false but staement II is correct

Explanation

Let y=`-tan^(-1)(x^(-1))+1`
`therefore (dy)/(dx)=(1)/(1+x^(2))(-1)x^(-2)=(1)/(1+x^(2))`
Since `(dy)/(dx)` is positive forall values of x .Therefore y is an increasing function of x
Hence option (A) is correct