if sqrt(1-x²⁾+ sqrt(1-y²) = a (x-y) prove dy/dx=sqrt((1-y²)/(1-x²))

Let x=sinA , y=sinB

Put it in given expression , cosA +cosB=a(sinA-sinB)

  2cos(A+B)/2 *cos(A-B)/2 =a*2Cos(A+B)/2 * Sin(A-B)/2

Cot(A-B)/2 =a

A-B=2cot^-1a

Sin-1x-sin-1y =2cot-1a

Now differentiate…

1/root 1-x2 - 1/root 1-y2 *dy/dx=0

dy/dx=root 1-y2/root 1-x2

Hope this will be clear...!!!