Question

prove that cos35+cos85+cos155=0

Answer 1

Cos 35°+cos85°+cos155°
= 2cos{(35°+85°)/2}cos{(35°-85°)/2}+cos(180°-25°) 
[cosC+cosD=2cos{(C+D)/2}cos{(C-D)/2}]
=2cos(120°/2)cos(50°/2)+cos{(90°×2)-25°}
=2cos60°cos25°+(-cos25°)
=2×(1/2)cos25°-cos25°
=0 (Proved)