Step-by-step explanation:
cos 20° cos 40° cos 60° cos 80°
<em>Simplify cos 60° to ½.</em>
½ cos 20° cos 40° cos 80°
<em>We can use double angle formula, sin(2θ) = 2 sin θ cos θ. Multiply and divide by 2 sin 20°.</em>
½ (2 sin 20° cos 20° cos 40° cos 80°) / (2 sin 20°)
½ (sin 40° cos 40° cos 80°) / (2 sin 20°)
<em>Multiply and divide by 2 and use double angle formula again.</em>
½ (2 sin 40° cos 40° cos 80°) / (4 sin 20°)
½ (sin 80° cos 80°) / (4 sin 20°)
<em>Multiply and divide by 2 and use double angle formula again.</em>
½ (2 sin 80° cos 80°) / (8 sin 20°)
½ (sin 160°) / (8 sin 20°)
<em>Use phase shift identity sin θ = sin(180−θ).</em>
½ (sin 20°) / (8 sin 20°)
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