`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]`

sin^(-1)x+sin^(-1)y=sin^(-1)(x sqrt(1-y^(2))+y sqrt(1-x^(2))) then find the area represented by the locus of point (x,y) if |x|<=1,|y|<=1

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

(dy)/(dx) if y=sin^(-1)x+sin^(-1)sqrt(1-x^(2)),x is 0 to 1

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

Prove that sin ^ (- 1) x + cos ^ (- 1) y = (tan ^ (- 1) (xy + sqrt ((1-x ^ (2)) (1-y ^ (2)))) ) / (y sqrt (1-x ^ (2)) - x sqrt (1-y ^ (2)))

(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

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

sqrt(1-y^(2))dx-sqrt(1-x^(2))dy=0 A) sin^(-1)x-cos^(-1)y=c B) sin^(-1)x-sin^(-1)y=c C) log(x+sqrt(1-x^(2)))=log(y+sqrt(1-y^(2)))+c D) x-y=c(1+xy)

underset0 If y=cos^(-1){x sqrt(1-x)+sqrt(x)sqrt(1-x^(2))} and

if,sin^(-1)x+sin^(-1)y+sin^(-1)z=pi then prove that x sqrt(1-x^(2))+y sqrt(1-y^(2))+z sqrt(1-z^(2))=2xyz