Question

cos(40°) + cos(80°) + cos(160°) + cos(240°) = ?

Answer 1

cos(40°) + cos(80°) + cos(160°) + cos(240°)

=> cos(40°)=cos (60-20)= cos 60°
cos 20+sin 60 sin20
=>cos 80°= cos (60+20)=cos 60°
cos 20+sin 60 sin20

=>cos 160° =cos (180-160)° = -cos 20°
=>cos 240 ° =cos (180+60)°=-cos 60°= -1/2

Since in 2nd Quadrant, Sin is +ve and
In 3rd Quadrant, tan is +ve

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
= -1/2

Therefore,


cos(40°) + cos(80°) + cos(160°) + cos(240°) = -1/2