Prove that `(cotA/2+cotB/2)(asin^2B/2+bsin^2A/2)=ccotC/2`

Explanation

`(cot.(A)/(2) + cot.(B)/(2)) (a sin^(2).(B)/(2) + b sin^(2).(A)/(2))`
`= [sqrt((s(s-a))/((s-b)(s-c))) + sqrt((s(s -b))/((s-a) (s-c)))] xx [(a (s -c) (s-a))/(ca) + (b(s-b) (s-c))/(bc)]`
`=sqrts. [((s-a) + (s-b))/(sqrt((s-a)(s-b)(s-c)))] ((s-c))/(c) [s -a + s - b]`
`= sqrts. [(c(s-c))/(sqrt((s-a) (s-b) (s-c)))]`
`= csqrt((s(s-c))/((s-a) (s-b))) = c cot.(C)/(2)`