In words, arctan(x) is the angle formed by a right triangle whose side opposite the angle and adjacent sides have ratio x/1. What is the measure of the other non-right angle in this hypothetical triangle, and what would the tangent of this other angle be?
Here's how I think of it... I rearranged the equation so that arctan(1/v) + arctan(v) = π/2
And I understand how the tan of, say ø = 1/v, making the tan of, say ß = v. That part makes sense. The part I'm getting confused on is the π/2, and what that does to the equation.
what's the sum of the angles in a triangle? Trig functions assume that one angle is 90 degrees. If one angle is [itex]\theta[/itex], then what's the other? Draw a triangle to aid you in this. Make one such that [itex]arctan(v)=\theta[/itex]. What's the other angle? What's the tangent of this other angle?