Question

Solve cos 20+cos 40+cos 140+cos 160​

Answer 1

Step-by-step explanation:

here remember that,

cos ( 180°- Φ ) = - cos Φ

or

cos ( π - Φ ) =- cos Φ

___________________________

cos20°+cos 40°+cos 140°+cos 160°

=)) cos 20° + cos 40° + (-cos (180°-140) )+ (- cos ( 180° - 160° ))

=)) cos 20° + cos40° + (-cos (40°))

+ (-cos (20°))

=)) cos 20° + cos 40° - cos 40° - cos 20°

= )) cos 20°-cos 20° + cos 40° - cos40°

= )) 0 + 0

= )) 0

therefor, cos20°+cos 40°+cos 140°+cos 160° = 0