Step-by-step explanation:
8 cos 80° cos 140° cos 160°
4 (2 cos 80° cos 140°) cos 160°
4 cos 160° (2 cos 80° cos 140°)
<em>Use product to sum formula.</em>
4 cos 160° (cos 60° + cos 220°)
4 cos 160° (½ + cos 220°)
2 cos 160° + 4 cos 220° cos 160°
2 cos 160° + 2 (2 cos 220° cos 160°)
<em>Use product to sum formula again.</em>
2 cos 160° + 2 (cos 60° + cos 380°)
2 cos 160° + 2 (½ + cos 380°)
2 cos 160° + 1 + 2 cos 380°
2 cos 160° + 1 + 2 cos 20°
<em>Use shift identity cos(180 − θ) = -cos θ.</em>
-2 cos 20° + 1 + 2 cos 20°
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