If `cos(x/2)cos(x/2^2) cos (x/2^3).......oo=sin x/x` then `1/2 tan(x/2)+1/2^2 tan (x/2^2)+1/2^3 tan (x/2^3)....oo`

If cos ((x) / (2)) cos ((x) / (2 ^ (2))) cos ((x) / (2 ^ (3))) ...... oo = (sin x ) / (x) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))) + ( 1) / (2 ^ (3)) tan ((x) / (2 ^ (3))) ... oo

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

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

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

Simplify tan^(-1)((cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2)))

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

If cos x = - (1)/(3) , x lies in III quardrnat, then find the values of sin(x/2), cos (x/2) and tan (x/2) .

Show that cos 2 x=cos ^(2) x-sin ^(2) x=2 cos ^(2) x-1=1-2 sin ^(2) x=(1-tan ^(2) x)/(1+tan ^(2) x)