If `sin^-1 x = -cos^-1(sqrt(1-x^2))`, then find `x`.

If y=(sin^(-1)x cos^(-1)((x^2)/2))/(1+x^2) then find the value of y(1/2) + y(1/sqrt2) + y(-1/2) + y(-1/sqrt2)

Prove that sin^(-1)x=cos^(-1) sqrt(1-x^2)

If f(x)=cos^(-1)((1)/(sqrt(13)))(2cos x-3sin x)+sin^(-1)((1)/(sqrt(13)))(2cos x+3sin x)wdot rt sqrt(1+x^(2)) then find (df(x))/(dx) at x=(3)/(4)

if: f(x)=(sin x)/(sqrt(1+tan^(2)x))-(cos x)/(sqrt(1+cot^(2)x)), then find the range of f(x)

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

If y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))) and 0

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

If y=cos^(-1)[sin sqrt(((1+x))/(2))]+x^(x) ,then find (dy)/(dx) at x=1

If f(x)=cos^(-1)(sin sqrt((1+x)/(2)))+x^(x) then at x=1,f'(x) is equal to

Evaluate int(sin^-1sqrt (x)-cos^-1sqrt (x))/(sin^-1sqrt (x)+cos^-1sqrt (x))dx