The value of `sum_(r=0)^(10)cos^3(rpi)/3` is equal to `1/4` (b) `1/8` (c) `-1/4` (d) `-1/8`

Options

A. `1//4`
B. `1//8`
C. `-1//4`
D. `-1//8`

Answer

D

Explanation

`sum_(r=0)^(10)cos^(3)((rpi)/(3))=(1)/(4)sum_(r=0)^(10)(3cos((rpi)/(3))+cos rpi)`
`=(1)/(4)[3(cos0+cos((pi)/(3))+.......+cos((10pi)/(3)))+(1-1+.....-1+1])`
`=(3)/(4)((cos((10pi)/(6))sin((11pi)/(6)))/(sin((pi)/(6))))+(1)/(4)=(1)/(8)`