`sin^(- 1)x+sin^(- 1)y=cos^(- 1) (sqrt(1-x^2) sqrt(1-y^2)-xy)` if `x in [0,1], y in [0,1]`

If sin^(-1) x + sin^(-1) y = pi/2 , prove that x sqrt(1-y^2) + y sqrt(1-x^2) =1 .

sin^(-1)(x^2/4+y^2/9)+cos^(-1)(x/(2sqrt2)+y/(3sqrt2)-2)

y=sin^(-1)(x/sqrt(1+x^2))+cos^(-1)(1/sqrt(1+x^2)), Find dy/dx

Find (dy)/(dx), if y=sin^(-1)[xsqrt(\ 1-x)-\ sqrt(x)\ sqrt(1-x^2)\ ]\

If y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)} and 0

y = sin^(-1)(1/sqrt(1+x^2)) + cos^(-1)(1/sqrt(1+x^2)) . find dy/dx .

If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),\ \ \ x \ \ is \ [0,1/2] , find (dy)/(dx) .

If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2) ,x is [-1/2,0] , find (dy)/(dx)

The solution of the inequality (log)_(1/2sin^(-1)x >(log)_(1//2)cos^(-1)x is x in [(0,1)/(sqrt(2))] (b) x in [1/(sqrt(2)),1] x in ((0,1)/(sqrt(2))) (d) none of these

If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2]) and 0 < x < 1, then find (dy)/(dx)