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

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)))

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

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

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

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

sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y),show(dy)/(dx)=sqrt((1-y^(2))/(1-x^(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]