Question

If A+B+C=180, and cos A=cos B cos C, show that 2 cot B cot C=1.

Answer 1

here 1800= pi now A+B+C=piA/2 + B/2= pi/2 – C/2cot[A/2+B/2]=cot[pi/2 - C/2]cotA/2.cotB/2 – 1/ cotA/2 + cotB/2= tanC/2= 1/ cotC/2therefore, cotA/2.cotB/2.cotC/2. =cotA/2 + cotB/2 +cotC/2this implies that  cotA/2 + cotB/2 + cotC/2 / cotA/2.cotB/2.cotC/2= 1so the answer is a) 1