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What is tan((pi)/(12))equal to ?...

What is `tan((pi)/(12))`equal to ?

A

`2-sqrt(3)`

B

`2+sqrt(3)`

C

`sqrt(2)-sqrt(3)`

D

`sqrt(3)-sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`"tan"(pi)/(12)="tan"((pi)/(3)-(pi)/(4))=(tanpi//3-tanpi//4)/(1+tanpi//3tanpi//4)`
`=(sqrt(3)-1-3+sqrt(3))/((1)^(2)-(sqrt(3))^(2))=(2(sqrt(3)-2))/(-2)=2-sqrt(3)`
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