यदि `A+B+C = pi` हो, तो सिद्ध कीजिए कि - `"tan"(B)/(2)"tan"(C )/(2)+"tan"(C )/(2)"tan"(A)/(2)+"tan"(A)/(2)"tan"(B)/(2)=1`.

Explanation

`(A+B+C)=pi rArr ((A)/(2)+(B)/(2)+(C )/(2))=(pi)/(2)`
`rArr " " (A)/(2)+(B)/(2)=(pi)/(2)-(C )/(2)`
`rArr " "tan ((A)/(2)+(B)/(2))=tan((pi)/(2)-(C )/(2))`
`rArr " " ("tan"(A)/(2)+"tan"(B)/(2))/(1-"tan"(A)/(2)"tan"(B)/(2))="cot"(C )/(2)`
`rArr " " ("tan"(A)/(2)+"tan"(B)/(2))/(1-"tan"(A)/(2)"tan"(B)/(2))=(1)/("tan"(C )/(2))`
`rArr " " "tan"(C )/(2)"tan"(A)/(2)+"tan"(B)/(2)"tan"(C )/(2)=1-"tan"(A)/(2)"tan"(B)/(2)`
`rArr " " "tan"(B)/(2)"tan"(C )/(2)+"tan"(C )/(2)"tan"(A)/(2)+"tan"(A)/(2)"tan"(B)/(2)=1`
`rArr " " L.H.S. = R.H.S. " "` इति सिद्धम्