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The value of tan20^@+tan40^@+sqrt3tan20^...

The value of `tan20^@+tan40^@+sqrt3tan20^@tan40^@` is

A

`sqrt(12)`

B

`(1)/(sqrt(3))`

C

`sqrt(3)`

D

`(sqrt(3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`becausetan60^(@)=tan(40^(@)+20^(@))`
`rArrsqrt(3)=(tan40^(@)+tan20^(@))/(1-tan40^(@)tan20^(@))`
`rArrsqrt(3)-sqrt(3)tan40^(@)tan20^(@)=tan40^(@)+tan20^(@)`
`thereforetan40^(@)+tan20^(@)+sqrt(3)tan40^(@)tan20^(@)=sqrt(3)`
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