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If cos^(-1).(x)/(2) + cos^(-1).(y).(3) =...

If `cos^(-1).(x)/(2) + cos^(-1).(y).(3) = (pi)/(6)`, then prove that `(x^(2))/(4) - (xy)/(2sqrt3) + (y^(2))/(9) = (1)/(4)`

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Verified by Experts

`cos^(-1) ((x)/(2)) + cos^(-1) ((y)/(3)) = (pi)/(6)`
`rArr cos^(-1) [(xy)/(6) - sqrt(1 -(x^(2))/(4)) sqrt(1 - (y^(2))/(9))] = (pi)/(6)`
`= rArr ((xy)/(6) -(sqrt3)/(2))^(2) = (1- (x^(2))/(4)).(1-(y^(2))/(9))`
`rArr (x^(2))/(4) - (xy)/(2sqrt3) + (y^(2))/(9) = (1)/(4)`
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