Question

if a+b+c = π/2 ,prove that cota+ cotb+cot c = cota cotb cotc . ​

Answer 1

$A+B+C=\frac{\pi }{2} \\A+B=\frac{\pi }{2}-C$

Taking cot x on both sides

$cot(A+B)=cot(\frac{\pi }{2} -C)\\\\\frac{cotAcotB-1}{cotA+cotB} =tanC\\\\\frac{cotAcotB-1}{cotA+cotB}=\frac{1}{cotC} \\\\cotC(cotAcotB-1)=cotA+cotB\\\\cotAcotBcotC-cotC=cotA+cotB\\cotAcotBcotC=cotA+cotB+cotC$

Hence Proved