Question

if A+B+C=pie
prove that-

CotA/2+CotB/2+CotC/2 = CotA/2CotB/2CotC/2

Answer 1

HINT:

A2+B2=π2−C2A2+B2=π2−C2

cot(A2+B2)=cot(π2−C2)=tanC2=1cotC2cot⁡(A2+B2)=cot⁡(π2−C2)=tan⁡C2=1cot⁡C2

Apply cot(x+y)=cotxcoty−1cotx+coty