(sin x^(2)(2,8+x^(2))/((21)^(2)+tan^(2)[(sqrt(1+a^(2)x^(2))-1)/(ax)]omega*x,1tan^(-1)cos x)ax

tan^(-1)((sqrt(1+a^(2)x^(2))-1)/(ax)) where x!=0, is

sin{tan^(-1)[(1-x^(2))/(2x)]+cos^(-1)[(1-x^(2))/(1+x^(2))]}=

Differentiate tan^(-1)((sqrt(1 + a^2 x^2) - 1)/(ax)) w.r.t.x.

Differentiate tan ^(-1)((sqrt(1+x^2 )-1)/x) w,r,t. tan ^(-1)x

y = "tan"^(-1)((sqrt(1 + a^2x^2 ) - 1)/(ax)) implies (1 + a^2x^2)y^('') + 2a^2 xy^' =

If tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))=k tan^(-1)(x/a) then k=

int(sin^(2)x*sec^(2)x+2tanx*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx= a) (cos^(2)x)(sin^(-1)x)+C b) (sin^(2)x)(sin^(-1)x)+C c) (sec^(2)x)(cos^(-1)x)+C d) (sec^(2)x)(tan^(-1)x)+C

int(sin^(2)x*sec^(2)x+2tan x*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx

sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))] is

sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))] is