Answer :
cos 40° + cos 80° + cos 160° + cos 240°
= (cos 40° + cos 80°) + (cos 160° + cos 240°)
= 2
+ 2
= 2cos 60° cos 20° + 2cos 200° cos 40°
= 2⋅ 1/2 ⋅cos 20° + 2cos (180 + 20)° cos 40°
= cos 20° - 2cos 20° cos 40°
= cos 20° - (cos (40° + 20°) + cos (40° - 20°))
= cos 20° - (cos 60° + cos 20°)
= - cos 60°
= - 1/2 (Ans)
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