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If alpha and beta the rots of the quadra...

If `alpha and beta` the rots of the quadratic equation, `x^(2)+x sintheta-2sintheta=0,theta in(0,(pi)/(2)),` then `(alpha^(12)+beta^(12))/((alpha^(-12)+beta^(-12))(alpha-beta)^(24))` is equal to

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6
`(alpha^(12) + beta^(12))/((alpha^(-12)+beta^(-12)(alpha -beta)^(24))) rArr (alpha^(12)beta^(12))/(alpha-beta)^(24) rArr (-2sin theta)^(1//2)/((sin theta)^(2) + 8 sin theta)^(12)`
`rArr (2^(12) sin^(12)theta)/(sin^(12)theta(sin theta + theta)^(12)) rArr 2^(12)/(sin theta + theta)^(12)`
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