" Q.3"tan^(-1)(x)/(sqrt(a^(2)-x^(2)))=

Differentiate tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|<(1)/(sqrt(3)) w.r.t tan ^(-1)((x)/(sqrt(1-x^(2))))

int(1+tan^(2)x)/(sqrt(tan^(2)x+3))

tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

Prove that tan^(-1)x+tan^(-1)((2x)/(1-x^(2)))=tan^(-1)((3x-x^(3))/(1-3x^(2)))|x|lt1/(sqrt(3))

Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , |x|<1/sqrt3 w.r.t tan^(-1)(x/sqrt(1-x^2))

int(x+2)/((x^(2)+3x+3)sqrt(x+1))dx is equal to a) (1)/(sqrt(3))tan^(-1)((x)/(sqrt(3)(x+1))) b) (2)/(sqrt(3))tan^(-1)((x)/(sqrt(3(x+1)))) c) (2)/(sqrt(3))tan^(-1)((x)/(sqrt(x+1))) d)None of these

If 3tan^(-1)((1)/(2+sqrt(3)))-(tan^(-1)1)/(x)=(tan^(-1)1)/(3) then x is equal to 1(b)2(c)3(d)sqrt(2)

tan^(-1)((1)/(sqrt(3))(tan x)/(2))=(1)/(2)cos^(-1)((1+2cos x)/(2+cos x))

show that, tan^(-1) ((1)/(sqrt(3)) tan ""(x)/(2))=(1)/(2) cos^(-1) ""((1+2 cos x)/(2+ cos x)).