cosπ/9+cos3π/9+cos5π/9+cos7π/9
=cos3π/9+cos(π-π/9)+cos(π-4π/9)+cos(π-2π/9)
=cosπ/3-(cos8π/9+cos4π/9+cos2π/9) *** cos(π-α) = -cosα
=1/2-(cos(π-π/9)+cos(3π/9+π/9)+cos(3π/9-π/9))
=1/2-(-cosπ/9+2*cos3π/9*cosπ/9) ***cos(a)cos(b) = 1/2*[cos(a+b)+cos(a-b)]
=1/2-(-cosπ/9+2*1/2*cosπ/9)
=1/2-(-cosπ/9+cosπ/9)
=1/2