tan^(-1)((1)/(sqrt(3))tan(x)/(2))=(1)/(2)cos^(-1)((1+2cos2x)/(2+cos x))

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)).

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

2 tan ^(-1) (sqrt((a-b)/(a+b))tan""(x)/(2))=cos^(-1)""(acos x+b)/(a+b cos x)

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

int(sinx)/(3+4cos^2x)\ dx a. log(3+4cos^2x)+C (b) 1/(2sqrt(3))tan^(-1)((cosx)/(sqrt(3)))+C (c) -1/(2sqrt(3))tan^(-1)((2"\ cos"x)/(sqrt(3)))+C (d) 1/(2sqrt(3))tan^(-1)((2"\ cos"x)/(sqrt(3)))+C

(tan3x)/(tan x)=(2cos2x+1)/(2cos2x-1)

int(sin x)/(3+4cos^(2)x)dx log(3+4cos^(2)x)+C(b)(1)/(2sqrt(3))tan^(-1)((cos x)/(sqrt(3)))+C(c)-(1)/(2sqrt(3))tan^(-1)((2backslash cos x)/(sqrt(3)))+C(d)(1)/(2sqrt(3))tan^(-1)((2backslash cos x)/(sqrt(3)))+C

cos ^(-1) ((3+5 cos x )/(5+3 cos x )) is equal to : a) tan ^(-1) ((1)/(2) tan ""(x)/(2)) b) 2 tan ^(-1) (2 tan ""(x)/(2)) c) (1)/(2) tan ^(-1) (2 tan ""(x)/(2)) d) 2 tan ^(-1) ((1)/(2) tan ""(x)/(2))