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

Options

A. 0
B. 1
C. 2
D. 10

Answer

C

Explanation

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`