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

Prove that : sin^(-1)x+sin^(-1)y=sin^(-1)(xsqrt(1-y^2)+ysqrt(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)))

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

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)(2xsqrt(1 - x^(2))),-(1)/sqrt(2) lt x lt (1)/sqrt(2)

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

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi then the value of xsqrt(1-x^(2))+ysqrt(1-y^(2))+zsqrt(1-z^(2))

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

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 .