In a triangle `tan A+ tan B + tan C=6` and `tan A tan B= 2,` then the values of `tan A, tan B` and `tan C` are

Options

A. 1,2,3
B. `3,2//3,7//3`
C. `4,1//2,3//2`
D. none of these.

Answer

A

Explanation

In triangle.
`tanA+tanB+tanC=tanA tan B tan C`
`rARr 6=2tanC`
or `tanC=3`
Also `an A+tanB=6-3=3`
By Eqs. I and ii, `tanA` and `tanB` are roots of `x^(2)-3x+2=0`.
thus,
`tanA,tanB=2,1` or `2,2` and `tanC=3`.