2tan^(-1)(x) has different representations with validity conditions: = sin^(-1)(2x/(1+x^2)) when |x| <= 1, = cos^(-1)((1-x^2)/(1+x^2)) when x >= 0, = tan^(-1)(2x/(1-x^2)) when |x| < 1. For sin^(-1) addition: sin^(-1)(x) + sin^(-1)(y) = sin^(-1)(xsqrt(1-y^2) + ysqrt(1-x^2)) when x^2 + y^2 <= 1 or (x >= 0, y >= 0). When x^2 + y^2 > 1 with both positive: sin^(-1)(x) + sin^(-1)(y) = pi - sin^(-1)(xsqrt(1-y^2) + y*sqrt(1-x^2)). The cos^(-1) addition formula: cos^(-1)(x) + cos^(-1)(y) = cos^(-1)(xy - sqrt(1-x^2)*sqrt(1-y^2)) when x + y >= 0. These conditions are cumbersome but tested in JEE.