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

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

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

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)

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

Prove the following "tan"^(-1)((1-x)/(1+x))-"tan"^(-1)((1-y)/(1+y))="sin"^(-1)((y-x)/(sqrt(1+x^(2))sqrt(1+y^(2)))) .

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

y=sin^(-1)((x)/(sqrt(1+x^(2))))+cos^(-1)((1)/(sqrt(1+x^(2))))

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