{cos(sin^(-1)x)}^(2)={sin(cos^(-1)x)^(2))^(2)

Prove that the identities,sin^(-1)cos(sin^(-1)x)+cos^(-1)sin(cos^(-1)x)=(pi)/(2)|x|<=1

If quad cos^(-1)x<1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+...oo=2 then the value of 12x^(2) is

If 0 lt cos^(-1)x lt 1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+…infty=2 , then the value of 12x is

If 0 < cos^(-1)x < 1 and 1+ sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+.....oo=2 then x equals

If 0ltcos^(-1)x lt 1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+…….oo=2 , then the value of 12x^(2) is

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?

If 0 < cos^-1(x) <1 and 1+sin(cos^(-1)x)+sin^2(cos^(-1)x)+sin^3(cos^(-1)x) + ..... =2 then the value of 12 x^2 is____

If 0

If 0 < cos^(-1)x < 1 and 1+sin(cos^(-1)x)+sin^2(cos^(-1)x)+sin^3(cos^(-1)x)....+oo=2, then the value of 12 x^2 is____.

sin^(2)(cos^(-1)x)+cos^(2)(sin^(-1)(sqrt(1-x^(2)))) = ________ (0ltxlt1)