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

The numerical value of `tan(pi/3)+2tan((2pi)/3)+4tan((4pi)/3)`is equal to

A

`-3sqrt3`

B

`-sqrt3`

C

`3sqrt3`

D

`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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CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
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