In any triangle ABC prove that `cot(A/2)+cot(B/2)+cot(C/2)=cot(A/2)cot – InterviewSolution

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1.	In any triangle ABC prove that `cot(A/2)+cot(B/2)+cot(C/2)=cot(A/2)cot(B/2)cot(C/2)`
Answer» Since, A + B + C = `pi` `implies (A)/(2) + (B)/(2) = (pi)/(2) - (C)/(2)` `implies cot ((A)/(2)+(B)/(2))=cot((pi)/(2)-(C)/(2))` `implies (cot.(A)/(2).cot.(B)/(2)-1)/(cot.(B)/(2)+cot.(A)/(2))=tan.(C)/(2)` `implies cot.(A)/(2).cot.(B)/(2).cot.(C)/(2)-cot.(C)/(2)=cot.(A)/(2)+cot.(B)/(2)` `implies cot.(A)/(2)+cot.(B)/(2)+cot.(C)/(2)=cot.(A)/(2)cot.(B)/(2)cot.(C)/(2)`

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