If `a_r=(cos2rpi+is in2rpi)^(1//9)` , then prove that `|a_1a_2a_3a_4a_5a_6a_7a_8a_9|=0.`

If alpha_r=(cos2rpi+isin2rpi)^(1/10) , then |(alpha_1, alpha_2, alpha_4),(alpha_2, alpha_3, alpha_5),(alpha_3, alpha_4, alpha_6)|= (A) alpha_5 (B) alpha_7 (C) 0 (D) none of these

If a_(r)="cos"(2rpi)/9+i "sin"(2rpi)/9 then value of the determinant Delta=|(1,a_(8),a_(7)),(a_(3),a_(2),a_(1)),(a_(6),a_(5),a_(4))| is

a_r={cos((2rpi)/9)+isin((2rpi)/9)} where r in {1,2,3 . . . 9} Find the value of abs((a_1,a_2,a_3),(a_4,a_5,a_6),(a_7,a_8,a_9))

If n be integer gt1, then prove that sum_(r=1)^(n-1) cos (2rpi)/n=-1

sum_(r=0)^(n) sin^(2)""(rpi)/(n) is equal to

The value of sum_(r=1)^(8)(sin(2rpi)/9+icos(2rpi)/9) , is

sum_(r=1)^(n-1)cos^(2)""(rpi)/(n) is equal to

Find sum_(r=1)^(10) cos^(3) rpi/3 .

The value of | sum_(r=1)^(23) cos ((rpi)/(12))| is

If a digit is chosen at random from the digits 1,2,3,4,5,6,7,8,9, then the probability that it is odd,is (4)/(9)( b) (5)/(9)(c)(1)/(9)(d)(2)/(3)