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`

Options

A. `(x^(2))/(a^(2))-(2xy)/(ab) cos alpha+(y^(2))/(b^(2))=sin^(2)alpha`
B. `(x^(2))/(a^(2))-(2xy)/(ab) sin alpha+(y^(2))/(b^(2))=cos^(2)alpha`
C. `(x^(2))/(a^(2))+(2xy)/(ab) cos alpha+(y^(2))/(b^(2))=sin^(2)alpha`
D. `(x^(2))/(a^(2))+(2xy)/(ab) sin alpha+(y^(2))/(b^(2))=cos^(2)alpha`

Explanation

We have
`sin^(-1)(x)/(a)+sin^(-1)(y)/(b)=alpha`
`rarr (pi)/(2)-cos^(-1)(x)(alpha)+(pi)/(2)-cos^(-1)(y)/(b)=alpha`
`rarr (xy)/(ab)-sqrt(1-(x^(2))/(z^(2))sqrt(1-y^(2))/(b^(2))=cos(pi-alpha)`
`rarr (x^(2))/(a^(2))+(2xy)/(ab)cos alpha+(y^(2))/(b^(2))=sin^(2)alpha`