If circumcentre of an equilateral triangle inscribed in `x^(2)/a^(2) + y^(2)b^(2) = 1,` with vertices having eccentric angles `alpna, beta, gamma,` respectively is `(x_(1), y_(1))` then `sum cos alpha cos beta + sum sin alpha sin beta =`

Options

A. `(9h^(2))/a^(2)+(9k^(2))/b^(2)+3/2`
B. `9h^(2)-9k^(2)+a^(2)b^(2)`
C. `(9h^(2))/a^(2)+(9k^(2))/b^(2)+3`
D. `(9h^(2))/(2a^(2))+(9k^(2))/(2b^(2))-3/2`

Answer

D