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

Show that cos^(-1) ((cosx+cos y)/(1+cos x.cosy))= 2tan^(-1)(tan(x/2).tan(y/2)) .

cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-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 ""(1)/(2)cos^(-1)""((5cos x+3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan""(x)/(2))

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

Show that : cos^-1(frac{cosx+cosy}{1+cosxcosy})=2tan^-1(tanfrac{x}{2}tanfrac{y}{2})

Prove that : (1)/(2) cos^(-1) ((1+ 2 cos x)/( 2+cosx) ) = tan^(-1) ((1)/(sqrt(3)) "tan" (x)/(2))

Prove that, tan^(-1)((3 sin 2x)/(5+3 cos 2x))+tan^(-1)((1)/(4) tan x)=x .

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