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Prove that (b + c -a) (cot.(B)/(2) + cot...

Prove that `(b + c -a) (cot.(B)/(2) + cot.(C)/(2)) = 2a cot.(A)/(2)`

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`(b+c -a) (cot.(B)/(2) + cot.(C)/(2))`
`= (2s - 2a) (sqrt((s(s -b))/((s-a)(s-c))) + sqrt((s(s -c))/((s-a) (s-b))))`
`= 2(s -a) sqrt s((s-b + s -c)/(sqrt((s-a) (s-b)(s-c))))`
`= 2(s -a) sqrts ((a)/(sqrt((s-a) (s-b) (s-c))))`
`= 2a sqrt((s(s-a))/((s-b)(s-c)))`
`= 2 a cot.(A)/(2)`
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