If circumcentre of an equilateral triang...

If circumcentre of an equilateral triangle inscribed in `x^2/a^2+y^2/b^2 =1` with vertices having eccentric angles `alpha , beta, gamma` respectively is `(x_1,y_1)` then `sum cos alpha cos beta + sum sinalpha sin beta = `

A

`(9x_1^2)/(a^2)+(9y_1^2)/(b^2)+3/2`

B

`9x_1^2 -9y_1^2 +a^2b^2`

C

`(9x_1^2)/(2a^2)+(9y_1^2)/(2b^2)-3/2`

D

`(9x_1^2)/(a^2)+(9y_1^2)/(b^2)+3`

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The correct Answer is:

C

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