`cos 40^0+cos 80^0+cos 160^0+cos 240^0=` `0` b. `1` c. `1//2` d. `-1//2`

Explanation

`-frac{1}{2}`


`cos 40^{circ}+cos 80^{circ}+cos 160^{circ}+cos 240^{circ}`


`=2 cos (frac{40^{circ}+80^{circ}}{2}) cos (frac{40^{circ}-80^{circ}}{2})+cos 160^{circ}-cos (180^{circ}+60^{circ})[ cos A+cos B=2 cos (frac{A+B}{2}) cos (frac{A-B}{2})]`


`=2 cos 60^{circ} cos (-20^{circ})+cos 160^{circ}-frac{1}{2}`


`=2 times frac{1}{2} cos 20^{circ}+cos 160^{circ}-frac{1}{2}`


`=-cos (180-20)^{circ}+cos 160^{circ}-frac{1}{2}`


`=-frac{1}{2}`