Question

co20+cos40+ cos140+cos160

Answer 1

cos(20) + cos(40) + cos(140) + cos(160)

$= \cos(20) + \cos(40) + \cos(180 - 40) + \cos(180 - 20)$
$= \cos(20) + \cos(40) + ( - \cos(40)) + (- \cos(20) )$
$= 0$
The final answer is 0.