y=tan^-1x+tan^-1 1/x

Question

graph and make conjecture

Answer 1

The graph is 2 straight horizontal lines with no point at x=0!

For x>0 the line is y=π/2 (or 90°) and for x<0 it is y=-π/2.

The conjecture is NOT a conjecture it is a conclusion: .arcsin(x) and arcsin(1/x) are complementary, i.e. the sum of these 2 angles is a right angle. To see why, draw a figure: a right triangle and mark one of the legs x and the other 1!