`arctanx + arctan(1/x) = pi/2 , x>0` Verify each identity

We will use the following formula:

`arctan(1/x)=pi/2-arctan(x),` if `x >0`

If we apply the above formula to the left side of our expression we get

`arctan(x)+arctan(1/x)=arctan(x)+pi/2-arctan(x)=pi/2`

                                                                                                          Q.E.D.

One should note that the formula from the beginning holds only for positive numbers. For negative numbers we have a slightly different formula holds.

`arctan(1/x)=-pi/2-arctan(x),` if `x<0`