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(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

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

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

prove that tan ((pi) / (4) + (1) / (2) cos ^ (- 1) ((a) / (b))) + tan ((pi) / (4) - (1) / (2) cos ^ (- 1) ((a) / (b))) = (b) / (a) cos ^ (- 1) ((cos x + cos y) / (1 + cos x cos y) ) = 2tan ^ (- 1) ((tan x) / (2) (tan y) / (2))

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