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Question

If A+B+C=π, prove that cot(A/2)+cot(B/2)+cot(C/2)=cot(A/2)cot(B/2)cot(C/2).

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Solution

We know tan(A/2)tan(B/2)+tan(B/2)tan(C/2)+tan(C/2)tan(A/2)=1
Dividing both sides by tan(A/2)tan(B/2)tan(C/2), we get
cotA2+cotB2+cotC2=cotA2cotB2cotC2.

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