The value of cos 0+ cos (π/9)+ cos (2 π/9)+ cos (3 π/9)+ cos (4 π/9)+ cos (5 π/9)+ cos (6 π/9)+ cos (7 π/9)+ cos (8 π/9) is

Question

The value of cos 0+ cos (π/9)+ cos (2 π/9)+ cos (3 π/9)+ cos (4 π/9)+ cos (5 π/9)+ cos (6 π/9)+ cos (7 π/9)+ cos (8 π/9) is (A) (1/2) (B) -(1/2) (C) 0 (D) 1

Tardigrade Admin · Accepted Answer

1+ cos (π/9)+ cos (2 π/9)+ cos (3 π/9)+ cos (4 π/9)- cos (4 π/9)- cos (3 π/9)- cos (2 π/9)- cos (π/9)=1

Q. The value of $cos 0 + cos \frac{π}{9} + cos \frac{2 π}{9} + cos \frac{3 π}{9} + cos \frac{4 π}{9} + cos \frac{5 π}{9} + cos \frac{6 π}{9} + cos \frac{7 π}{9} + cos \frac{8 π}{9}$ is

$\frac{1}{2}$

$- \frac{1}{2}$

0

1

$1 + cos \frac{π}{9} + cos \frac{2 π}{9} + cos \frac{3 π}{9} + cos \frac{4 π}{9} - cos \frac{4 π}{9} - cos \frac{3 π}{9} - cos \frac{2 π}{9} - cos \frac{π}{9} = 1$

Q. The value of cos0+cos9π​+cos92π​+cos93π​+cos94π​+cos95π​+cos96π​+cos97π​+cos98π​ is

21​

−21​

0

1

1+cos9π​+cos92π​+cos93π​+cos94π​−cos94π​−cos93π​−cos92π​−cos9π​=1

Q. The value of $cos 0 + cos \frac{π}{9} + cos \frac{2 π}{9} + cos \frac{3 π}{9} + cos \frac{4 π}{9} + cos \frac{5 π}{9} + cos \frac{6 π}{9} + cos \frac{7 π}{9} + cos \frac{8 π}{9}$ is

$\frac{1}{2}$

$- \frac{1}{2}$

$1 + cos \frac{π}{9} + cos \frac{2 π}{9} + cos \frac{3 π}{9} + cos \frac{4 π}{9} - cos \frac{4 π}{9} - cos \frac{3 π}{9} - cos \frac{2 π}{9} - cos \frac{π}{9} = 1$