If `cos^(-1)x/a+cos^(-1)y/b=alpha,` prove that `(x^2)/(a^2)-2(x y)/(a b)cosalpha+(y^2)/(b^2)=sin^2alpha`

If cos^(-1)(x/a) + cos^(-1) (y/b) = alpha show that : (x^2)/(a^2) - (2xy)/(ab) cos alpha + (y^2)/(b^2) = sin^(2) alpha .

If cos^(-1)((x)/(2))+cos^(-1)((y)/(3))=alpha then prove that 9x^(2)-12xy cos alpha+4y^(2)=36sin^(2)alpha

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 cos^(-1) x - cos^(-1). y/2= alpha ", then " 4x^(2) - 4xy cos alpha + y^(2) is equal to

If cos^(-1)x-cos^(-1)y=alpha, then x^(2)+y^(2)-2xy cos alpha is equal to