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))

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

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

Sin^(-1)(xsqrt(1-y^(2))+ysqrt(1-x^(2)))=

prove that . Tan ^(-1) x- tan ^(-1 )y = cos ^(-1) (1+xy)/(sqrt((1+x^(2))(1+y^(2)))).

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))))

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , prove that: xsqrt(1-x^2)+ysqrt(1-y^2)+zsqrt(1-z^2)=2x y z

Prove the followings : If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi then xsqrt(1-x^(2))+ysqrt(1-y^(2))+zsqrt(1-z^(2))=2xyz .

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