Question

if A+B+C=180
PROVE-- Cota/2*cotb/2 + cotb/2*cotc/2 + cotc/2*cota/2=1

Answer 1

If ABC is a triangle 
A + B + C = π 
=> A/2 + B/2 = π/2 - C/2 
=> tan (A/2 + B/2) = tan (π/2 - C/2) 
=> (tan A/2 + tanB/2) / (1 - tan A/2 tan B/2) = cot C/2 
=> (cot A/2 + cot B/2) / (cot A/2 cot B/2 - 1) = cot C/2 
=> cot A/2 + cot B/2 + cot C/2 = cot A/2 cot B/2 cot C/2 
Of course its only true when ABC are angles of a triangle