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The numerical value of tanpi/3+2tan(2pi)...

The numerical value of `tanpi/3+2tan(2pi)/3+4tan(4pi)/3+8tan(8pi)/3` is equal to `-5sqrt(3)(b)-5/(sqrt(3))` (c) `5sqrt(3)` (d) `5/(sqrt(3))`

A

`-5sqrt3`

B

`-5/sqrt3`

C

`5sqrt3`

D

`5/sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
A
`tan.pi/3+2tan.(2pi)/3+4tan.(4pi)/3+8tan.(8pi)/3`
`=tan.pi/3+2tan(pi-pi/3)+tan.pi/3+4tan(pi-pi/3)+tan.pi/3+8tan(3pi-pi/3)`
`=tan.pi/3-2tan.(pi)/3+4tan.(pi)/3-8tan.(pi)/3`
`=-5tan.pi/3=-5sqrt3`
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