[cos^(-1)sqrt((1+tan x)/(2));AA0

cos ^ (- 1) sqrt ((1 + cos x) / (2)); AA0

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

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

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

show that , (1) /(2) tan ^(-1) x = cos^(-1) sqrt((1+sqrt(1+x^(2)))/(2sqrt(1+x^(2)))).

(d)/(dx)[tan^(-1)sqrt((1+(cos x)/(2))/(1-(cos x)/(2))))

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

show that, tan^(-1) ((1)/(sqrt(3)) tan ""(x)/(2))=(1)/(2) cos^(-1) ""((1+2 cos x)/(2+ cos x)).

Show that : tan (cos^(-1)x) = (sqrt(1-x^(2)))/x

prove that , tan(2tan ^(-1) sqrt((1+cos theta )/(1- cos theta )))+tan theta =0