2tan^(-1)(x) has different representations with validity conditions: = sin^(-1)(2$\frac{x}{1+x^2}$) when |x| <= 1, = cos^(-1)$\frac{(1-x^2}{(1+x^2)}$) when x >= 0, = tan^(-1)(2$\frac{x}{1-x^2}$) 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.