If `A+B+C=pi` , prove that `cotA+cotB+cotC-cos e cAdotcos e cBdotcos e cC=cotAdotcotBdotcotCdot`

Explanation

`cot A+cot B+cot C-co sec A. co sec B. co sec C`
`=(Cos A)/(sinA)+(cos B)/(sin B)+(Cos C)/(sin C)-(1)/(sin A.sinB.sinC)`
`{sin C(cos A sin B sin C+cos B sin C sin A)`
`=(+cos C sin A sin B-1})/(sin A sin B sin C)`
`((sinC(cosAsinB+cosBsinA)+cosCsinAsinB-1))/(sinA sin B sinC)`
`(sin Csin(A+B)+cosCsin A sin B-1)/(sin A sin B sin C)`
`=(sin^(2)C+cosC sinA sin B-1)/(sin A sin B sin C)`
`{becauase sin(A+B)=sin(pi-C)=sinC}`
`=(cos C. sin A sin B-cos^(2)C)/(sin A sin B sin C)`
`=(cos C(sin A sin B -cos(pi-(A+B)))/(sin A sin B sin C)`
`=(cos C.sin A sin B+cos(A+B)))/(sin A sin B sin C)`
`=(cos C.cos A. cos B)/(sin A sin B sinC)`
`=cot A. cot B . cot C`