cos(2tan^(-1)x)=(y)/(2)," thom "x=?

If y=tan^(-1) sqrt((1+cos ((x)/(2)))/(1-cos ((x)/(2))),"then " dy/dx=

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

If cos ^ (- 1) x + cos ^ (- 1) y = (pi) / (2), tan ^ (- 1) x-tan ^ (- 1) y = 0 then x ^ (2) + xy + y ^ (2) =

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

If quad (2tan x)/(1+tan^(2)x))=((cos2x+1)(sec^(2)x+2tan x))/(2) then domain and range of y=f(x) are given by

f((2tan x)/(1+tan^(2)x))=((cos2x+1)(sec^(2)x+tan x))/(2) then f(x)=

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

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