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

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

tan^(-1)[(2cos x-3sin x)/(3cos x+2sin x)]

Simplify tan^(-1)[(a cos x-b sin x)/(b cos x+a sin x)], if (a)/(b)tan x>-1

Simplify: (sin^(6)x+cos^(6)x)/(sin^(2)x cos^(2)x)

If sin^(-1)x in (0, (pi)/(2)) , then the value of tan((cos^(-1)(sin(cos^(-1)x))+sin^(-1)(cos(sin^(-1)x)))/(2)) is :

(sin2x)/(1+cos2x)=tan x

solve tan(x)/(2)=(1-cos x)/(sin x)

f_(1)(x)=sin^(-1)(cos(sin^(2)x)),f_(2)(x)=cos^(-1)(sin(cos^(2)x)),f_(3)(x)=sin^(-1)(cos^(2)x)),f_(4)(x)=cos^(-1)(sin^(2)x)* Then which of the following is/are correct?

Simplify sin cot^(-1)tan cos^(-1)x,x>0

((sin x+cos x)^(2))/((sin x-cos x)^(2))