Three complementary identities connect inverse co-function pairs: sin^(-1)(x) + cos^(-1)(x) = pi/2 for all x in [-1, 1], tan^(-1)(x) + cot^(-1)(x) = pi/2 for all real x, and sec^(-1)(x) + csc^(-1)(x) = pi/2 for |x| >= 1. These allow instant conversion between co-function inverses. For reciprocal arguments: sin^(-1)$\frac{1}{x}$ = csc^(-1)(x) for |x| >= 1, cos^(-1)$\frac{1}{x}$ = sec^(-1)(x) for |x| >= 1, and tan^(-1)$\frac{1}{x}$ = cot^(-1)(x) for x > 0 (but = cot^(-1)(x) - pi for x < 0, or equivalently -pi/2 - tan^(-1)(x) for x < 0). The sign-dependent behavior for negative arguments is a frequent source of errors.