tan^(-1)((1)/(13)tan(x)/(2))=(1)/(2)cos^(-1)((1+2cos x)/(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))

If tan^(-1)(1)/(4)+tan^(-1)(2)/(9)=(1)/(2)cos^(-1)x then x is equal to

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))

int(1)/(1+3cos^(2)x)dx=(1)/(2)tan^(-1)((tan x)/(2))+c

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))

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

tan((pi)/(4)+(1)/(2)cos^(-1)x)+tan((pi)/(4)-(1)/(2)cos^(-1)x),x!=0 is equal to