Given that tan ` alpha and tan beta` are the roots of the equation `x^(2)+bx+c=0` with `bne0`.
What is `tan(alpha+beta)` equal to ?

Options

A. `b(c-1)`
B. `c(b-1)`
C. `c(b-1)^(-1)`
D. `b(c-1)^(-1)`

Answer

D

Explanation

`x^(2)+bx+c=0 " " b ne0`
`thereforetanalphaandtanbeta`are roots of equation.
`thereforetanalpha+tanbeta=(-b)/(1)=-b` . . . (1)
`thereforetanalphatanbeta=(c)/(1)=c`
`tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)=(-b)/(1-c)`
`=b(c-1)^(-1)`