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