Question

Cos40+cos80+cos160+cos240=

Answer 1

cos 40=cos (60-20)=cos 60 cos 20+sin 60 sin20
cos 80= cos (60+20)=cos 60 cos 20- sin 60 sin 20
cos 160=cos (180-160)= -cos 20
cos 240=cos (180+60)=-cos 60=-1/2
in second quant sin is positive
3rd quant tan is positive
sub all
cos 60 cos 20 + sin 60 sin 20+ cos 60 cos 20 - sin 60 sin 20-cos 20-1/2
= 2cos 60 cos 20- cos 20 -1/2
=cos 20(2(1/2)-1)-1/2
cos 20(0)-1/2
ans=-1/2