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In any triangle ABC sum (sin^2A+sinA+1)/...

In any triangle ABC `sum (sin^2A+sinA+1)/sinA` is always greater than or equal

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In triangle ABC,
`sum (sin^2A + sin A+1)/sinA = (sin^2A + sin A+1)/sinA+ (sin^2B + sin B+1)/sinB+ (sin^2C + sin C+1)/sinC`
`=sinA+1/sinA+sinB+1/sinB+sinC+1/sinC+3`
As, `sin theta` in any triangle is always greater than `0`.
`:. sin theta + 1/sin theta ge 2`.
`:. sinA+1/sinA+sinB+1/sinB+sinC+1/sinC ge6 ` `=>sinA+1/sinA+sinB+1/sinB+sinC+1/sinC+3 ge 9`
Thus,
...
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