Let A, B and C are the angles of a plain triangle and `tan(A/2)=1/3,tan(B/2)=2/3` .then `tan(C/2)` is equal to

Options

A. `1//3`
B. `2//3`
C. `2//9`
D. `7//9`

Answer

D

Explanation

Given, `A+B+C=pi`
`implies (A+B)/(2)=(pi)/(2)-(C)/(2)`
`impliestan((A+B)/(2))=tan((pi)/(2)-(C)/(2))=cot.(C)/(2)`
`implies(tan.(A)/(2)+tan.(B)/(2))/(1-tan.(A)/(2)tan.(B)/(2))=cot.(C)/(2)`
`implies ((1)/(3)+(2)/(3))/(1-(1)/(3)xx(2)/(3))=cot.(C)/(2)[becausetan.(A)/(2)=(1)/(3),tan.(B)/(2)=(2)/(3)("given")]`
`impliescot.(C)/(2)=(9)/(7)`
`impliestan.(C)/(2)=(7)/(9)`