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

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

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

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

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

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

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))

Which of the following is/are correct? tan[cos^(-1)(4)/(5)+tan^(-1)(2)/(3)]=(17)/(6)cos[tan^(-1)(1)/(3)+tan^(-1)(1)/(2)]=(1)/(sqrt(2))cos2tan^(-1)((1)/(3))+cos(tan^(-1)2sqrt(2))=(14)/(15)cos[2cos^(-1)(1)/(5)+sin^(-1)(1)/(5)]=-(2sqrt(6))/(6)

1.What is the value of tan[(1)/(2)cos^(-1)((3)/(5))]+tan[(1)/(2)cos^(-1)((4)/(5))] ?