Question

Cotb.cotc+cotc.cota+cota.cotb=1

Answer 1

A + B = 180-C
take tan of both sides
(tan A + tan B)/(1-tan A tan B) = - tan C
or tan A + tan B + tan C = tan A tan B tan C
deviding both sides by Tan A tan B tan C
we get 1/tan B 1/ tan C + 1/tan A 1/ tan C + 1/ tan A 1/tan B = 1
or cot B cot C+ cot A cot C + cot A cot B = 1