tan^(-1)(x) + tan^(-1)(1/x) = pi/2 when x > 0, and = -pi/2 when x < 0. This comes from cot^(-1)(x) = tan^(-1)(1/x) for x > 0. For x < 0, cot^(-1)(x) = pi + tan^(-1)(1/x), so the relationship differs. Always check the sign of x before using this identity.