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. `(9x_(1)^(2))/(2a^(2))+(9y_(1)^(2))/(2b^(2))-(3)/(2)`
B. `(x_(1)^(2))/(2a^(2))+(y_(1)^(2))/(2b^(2))-(5)/(2)`
C. `(x_(1)^(2))/(9a^(2))+(y_(1)^(2))/(9b^(2))-(5)/(9)`
D. `(x_(1)^(2))/(a^(2))+(y_(1)^(2))/(b^(2))-(1)/(2)`

Answer

A