Question

The numerical value of `tan(pi/3)+2tan((2pi)/3)+4tan((4pi)/3)+8tan((8pi)/3)` is equal to (A) `-5sqrt(3)` (B) `-5/(sqrt3)` (C) `5sqrt(3)` (D) `5/(sqrt3)`

Answer 1

`tan(x/3)=tan60=sqrt3`
`=sqrt3+2*(-sqrt3)+4*sqrt3+8*(-sqrt3)`
`=5sqrt3-10sqrt3`
`=-5sqrt3`.