If `sin^-1 (x/a) +sin^-1 (y/b) = sin^-1 (c^2/(ab))` then prove that `b^2x^2 +2xysqrt(a^2b^2-c^2) = c^4-a^2y^2-2x^2y^2`

If sin^(-1)x/a +sin^(-1)y/b = sin^(-1) c^(2)/ab show that b^(2)x^(2) + 2xy sqrt(a^(2)b^(2)-c^(4)) +a^(2)y^(2) = c^(4)

If sin^(-1) x + sin^(-1) y = pi/2 , prove that x sqrt(1-x^2) + y sqrt(1-y^2) =1 .

If cos ^(-1) .(x)/(a)+ cos ^(-1). (y)/(b) = theta then prove that (x^(2))/(a^(2)) -(2xy)/(ab) . cos theta+ (y^(2))/(b^(2)) = sin ^(2) theta .

If sin^-1 x+sin^-1 y+sin^-1 z= pi prove that: x^4+y^4+z^4+4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^20

x=a sin theta , y=btantheta so prove that a^2/x^2-b^2/y^2=1

If sin^(-1)x + sin^(-1)y = pi/2 prove that 2(x^(2) -x^(2)y^(2) + y^(2)) = 1 + x^(4) +y^(4) .

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

If x = a cos theta - b sin theta and y = a sin theta + b cos theta, prove that x^2 + y^2 = a^2 + b^2.

If x=a sin theta and y=b tan theta, then prove that (a^(2))/(x^(2))-(b^(2))/(y^(2))=1

If (cos ^ (4) x) / (cos ^ (2) y) + (sin ^ (4) x) / (sin ^ (2) y) = 1 then prove that (cos ^ (4) y) / (cos ^ (2) x) + (sin ^ (4) y) / (sin ^ (2) x) = 1