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Given a triangle A B C with sides a=7, b...

Given a triangle `A B C` with sides a=7, b=8 and c=5. Find the value of expression `(sinA+sinB+sinC)(cot A/2+cotB/2+cotC/2)`

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`(sin A + sin B + sin C) (cot.(A)/(2) + cot.(B)/(2) + cot.(C)/(2))`
`= ((a)/(2R) + (b)/(2R) + (c)/(2R)) ((s(s -a))/(Delta) + (s(s-b))/(Delta) + (s(s -c))/(Delta))`
`= ((a + b+ c)/(2R)) ((s(3s - a - b -c))/(Delta))`
`= ((2s)/(2R)) ((s^(2))/(Delta)) = (s^(3))/(RDelta)`
`= (s^(3))/(R(abc)/(4R)) = (4s^(3))/(abc)`
`= (4((a + b+ c)/(2))^(3))/(abc) = (4((7 + 8 + 5)/(2))^(3))/(7 xx 8 xx 5) = (100)/(7)`
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