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P(x)=(x-cos36^@)(x-cos84^@)(x-cos156^@) ...

P(x)=`(x-cos36^@)(x-cos84^@)(x-cos156^@)` then coefficient of `x^2` is

A

`(sqrt(5) - 1)/(4)`

B

`(sqrt(5) - 1)/(16)`

C

`(sqrt(5) + 1)/(16)`

D

`(1)/(16)`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`-cos36^(@) cos84^(@) cos156^(@)`
`= cos(60^(@) - 24)cos(60 + 24)cos24`
`= (1)/(4)cos(3 xx 24) = (cos72)/(4) = (sqrt(5) - 1)/(16)`
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