Question

If A + B + C = π ,prove that cot B cot C + Cot C CotA + Cot A cot B = 1

Answer 1

A + B + C = π

= ( A + B ) = ( π - C )

= Cot ( A + B ) = cot ( π - C) = - Cot C

= Cot A Cot B -1 /cot A + cot B = - Cot C

= cot A cot B - 1 = - cot C Cot A - Cot B cot C

= cot B cot C + Cot C CotA + Cot A cot B = 1

Answer 2

A + B + C = {pi}
A + B = {pi} - C
take both sides, cot
cot(A + B) = cot [{pi} - C]
(cotA.cotB-1)/(cotB+cotA)= - cotC
cotA.cotB -1 = -cotB.cotC -cotA.cotC
cotA.cotB + cotB.cotC +cotC.cotA = 1 \\