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The value of tan (pi/16)+2tan(pi/8)+4 is...

The value of `tan (pi/16)+2tan(pi/8)+4` is equal to

A

`cot ""(pi)/(8)`

B

`cot""(pi)/(16)`

C

`cot""(pi)/(16)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We know that `tan theta =cot theta -2 cot 2theta`
`thereforetan""(pi)/(16)+2 tan""(pi)/(8)+4`
`(cot""(pi)/(16)-2cot""(pi)/(8))+2(cot""(pi)/(8)-2cot""(pi)/(4))+4=cot""(pi)/(16)`
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