Transform `sin^(-1)x` in other inverse trigonometric function, where `x in (-1,\ 1)"\"{0}`

Write tan^(-1) x, x gt 0 in the form of other inverse trigonometric function

Solve the trigonometric equation: cos x+sin x=1

cos^(-1) (cos (-5)) + sin^(-1) (sin(6)) - tan^(-1)(tan (12)) is equal to : (The inverse trigonometric functions take the principal values)

cos^(-1) (cos (-5)) + sin^(-1) (sin(6)) - tan^(-1)(tan (12)) is equal to : (The inverse trigonometric functions take the principal values)

Computer the inverse of the function : f (x) = (1+x)/(1-x)

If alpha=3sin^(-1)((6)/(11)) and beta=3cos^(-1)((4)/(9)) where the inverse trigonometric functions take only the principal values,then the correct option(s) is (are)

Solve the trigonometric equation: sqrt(3)cos x-sin x=1

The number of real solutions of the equation sin^(-1)(sum_(i=1)^oox^(i+1)-xsum_(i=1)^oo(x/2)^i)=pi/2-cos^(-1)(sum_(i=1)^oo(-x/2)^i-sum_(i=1)^oo(-x)^i) lying in the interval (-1/2,1/2) is ____. (Here, the inverse trigonometric function =sin^(-1)x and cos^(-1)x assume values in [pi/2,pi/2] and [0, pi] , respectively.)