If `sin^-1(a^2 x^2+b^2 y^2)+cos^-1|a x+b x|=pi.` if `ab < 0,`then which of the following can be true-

Let (x, y) be such that sin^-1 (ax) + cos^-1 (y)+ cos^-1 (bxy)=pi/2 If a=1 and b=2 , then (x,y)

Let (x, y) be such that sin^-1 (ax) + cos^-1 (y)+ cos^-1 (bxy)=pi/2 If a=1 and b=1 , then (x,y)

Let (x, y) be such that sin^-1 (ax) + cos^-1 (y)+ cos^-1 (bxy)=pi/2 If a=1 and b=0 , then (x,y)

Let (x, y) be such that sin^-1 (ax) + cos^-1 (bxy)=pi/2 If a=1 and b=0 , then (x,y)

Let (x,y) be such that sin^(-1)(ax)+cos^(-1)(bxy)=(pi)/(2) If a=1 and b=0, then (x,y)

If sin^-1 x + sin^-1 y = (2pi)/3, then cos^-1 x + cos^-1 y =

"If "y=tan^(-1)((a cos x- b sin x)/(b cos x + a sin x)), (b/a)tanx lt 1"where "-(pi)/(2)ltxlt(pi)/(2)" then find "(dy)/(dx).

If cos^(-1) . x/a - sin^(-1). y/b = theta (a , b , ne 0) , then the maximum value of b^(2) x^(2) + a^(2) y^(2) + 2ab xy sin theta equals