Question

यदि `A+B+C =pi,` सिद्ध कीजिए कि
`cotA cot B+cot B cot C +cot C cot A=1`

Answer 1

हम जानते हैं कि `A+B+C=pi`
`rArr" "A+B=pi-C`
`rArr" "cot(A+B)=cot(pi-C)=-cotC`
`rArr" "(cotAcotB-1)/(cotA+cotB)=-cotC`
`rArr" "cotAcotB-1=-cot C cot A-cot B cot C`
`rArr" "cotB cot C+cot C cot A +cot A cot cot B =1`
`rArr" "cot A cot B +cot B cot C + cot C cot A=1`