(2y)sin(2tan^(-1)sqrt((1-21)/(1+21)))

If y = tan^(-1) {(x)/(1 + sqrt(1 - x^(2)))} + sin { 2 tan^(-1) sqrt((1 - x)/(1 + x))}, "then" (dy)/(dx) =

(1)/(sqrt(21+4x-x^(2)))

If x=sin(2tan^(-1)2sqrt3)and y=sin((1)/(2)tan^(-1).(12)/(5)) , then

The expression (1)/(sqrt(2)){(sin tan^(-1)cos tan^(-1)t)/(cos tan^(-1)sin cot^(-1)sqrt(2)t)}*{sqrt((1+2t^(2))/(2+t^(2)))}

If x in[-1/2,1] then sin^(-1)(sqrt(3)/(2)x-1/2sqrt(1-x^(2)))

If x in[-1/2,1] then sin^(-1)(sqrt(3)/(2)x-1/2sqrt(1-x^(2)))