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The value of 4 cos 18^(@)-(3)/(cos 18^(@...

The value of 4 `cos 18^(@)-(3)/(cos 18^(@))-2` tan `18^(@)` is equal to

A

0

B

1

C

`sqrt(5)-1`

D

`sqrt(5)+1`

Text Solution

Verified by Experts

The correct Answer is:
A
`4 cos 18^(@)-(3)/(cos 18^(@)-2tan 18^(@)`
`=(4 cos^(2)18^(@)-3-2sin 18^(@))/(cos 18^(@))`
`=(2(1+cos 36^(@))-2 sin 18^(@)-3)/(cos 18^(@))`
`=(2(1+cos 36^(@))-2 sin 18^(@)-3)/(cos 18^(@))`
`=(2(1+co 36^(@)-sin 18^(@))-3)/(cos 18^(@))`
`=(2(1+cos 36^(@)-sin 18^(@))-3)/(cos 18^(@))=0`
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