If A, B and C are angles of a triangle such than tan A = 1, tan B = 2, then what is the value of tan C ?

Options

A. 0
B. 1
C. 2
D. 3

Answer

C

Explanation

In any triangle ABC, A + B + C = `pi`
or, `A + B = pi = C`
so, `tan(A+B)=tan(pi-C)`
or, `-tan C = tan(A+B)`
so, `tan C = -tan(A+B)`
`-(tan A + tan B)/(1-tan A. tan B)`
As given, tan A = 1, and tan B = 2
putting these values,
`tan C =-(1+3)/(1-1xx3)=(4)/(2)=2`