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What is the value of tan18^(@) ?...

What is the value of `tan18^(@)` ?

A

`(sqrt(5)-1)/(sqrt(10+2sqrt(5)))`

B

`(sqrt(5)-1)/(sqrt(10+sqrt(5)))`

C

`(sqrt(10+2sqrt(5)))/(sqrt(5)-1)`

D

`(sqrt(10+sqrt(5)))/(sqrt(5)-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`tan18^(@)=(sin18^(@))/(cos18^(@))=((sqrt(5)-1)/(4))/(sqrt(10+2sqrt(5))/(4))=(sqrt(5)-1)/(sqrt(10+2sqrt(5)))`
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