" Let "sin^(-1)x+sin^(-1)y+-sin^(-1)(x sqrt(1-y^(2))+y sqrt(1-x^(2)))=k pi," then find the possible value(s) of "k

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

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

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]

Let k[f(x)+f(y)]=f(x sqrt(1-y^(2))+y sqrt(1-x^(2))) then k=:

Prove the following: sin^-1x-sin^-1y = sin^-1[x(sqrt(1-y^2))-y(sqrt(1-x^2))]

sin^-1 x+ sin^-1 y = sin^-1[x 1-y^2 + y 1- x^2]

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

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]