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In Q. No. 121, 1-sum(k=1)^(9)cos(2kpi)/1...

In Q. No. 121, `1-sum_(k=1)^(9)cos(2kpi)/10` equals

A

0

B

1

C

2

D

10

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, `1,z_(1),z_(2),………z_(9)` are `10^(th)` roots of unity which are roots of the equation `z^(10)-1=0`.
`therefore` Sum of the roots`= -("Coeff. Of"z^(9))/("Coeff.of"z^(10))=0`
`rArr 1+z_(1)+z_(2)+………..+z_(9)=0`
`rArr "Re"(1)+"Re")(z_(2))+......+"Re"(z_(9))=0`
`rArr 1-sum_(k=1)^(9)"Re")(z_(2))=1-(-1)`
`rArr 1-sum_(k=1)^(9)cos(2kpi)/10)=2`
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