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The value of tan(pi/3)+2tan((2pi)/3)+4co...

The value of `tan(pi/3)+2tan((2pi)/3)+4cot((4pi)/3)+8tan((8pi)/3)` is

A

`-5sqrt(3)`

B

`-5/(sqrt3)`

C

`5sqrt(3)`

D

`5/(sqrt3)`

Text Solution

Verified by Experts

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