Prove that `cos^(-1)((cosx+cosy)/(1+cosxcosy))=2tan^(-1)(tan(x/2)tan(y/2))`

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

(sinx-siny)/(cosx+cosy)=tan(x-y)/(2)

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))

Prove that tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)

Prove that: tan^(-1){(a cosx-b sinx)/(b cosx+a sinx)} =tan^(-1)((a)/(b))-x

Prove that: i) tan^(-1)(sqrt(x)+sqrt(y))/(1-sqrt(xy))=tan^(-1)sqrt(x)+tan^(-1)sqrt(y) ii) tan^(-1)(x+sqrt(x))/(1-x^(3//2))=tan^(-1)x+tan^(-1)sqrt(x) iii) tan^(-1)(sinx)/(1+cosx)=x/2

Prove that tan^(-1)(sqrt((1-cosx)/(1+cosx))=x/2, x lt pi .

Prove that 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x)=tan^(-1)x(x!=0)dot

Prove that : tan^(-1)((x-y)/(1+xy)) + tan^(-1)((y-z)/(1+yz)) + tan^(-1)( (z-x)/(1+zx)) = tan^(-1)((x^2-y^2)/(1+x^2y^2))+tan^(-1)((y^2-z^2)/(1+y^2z^2))+tan^(-1)((z^2-x^2)/(1+z^2x^2))

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