LHS = \(\cos20° \cos40°\cos 80°\)
\(= \frac 12[2\cos20° \cos40°]\cos80°\)
\(= \frac 12[\cos(20° + 40°) + \cos(20° - 40°)] \cos 80°\)
\(= \frac 12 [\cos60° + \cos(-20°)] \cos80° \)
\(= \frac 12\cos 80° [\frac 12 + \cos20°]\)
\(= \frac 14 \cos 80° + \frac 12 \cos 80° \cos 20°\)
\(= \frac 14 \cos 80° + \frac 14[ 2\cos 80° \cos 20°]\)
\(= \frac 14 \cos 80° + \frac 14[ \cos (80°+20°) + \cos (80°-20°]\)
\(= \frac 14\cos 80° + \frac 14[\cos100° + \cos60°]\)
\(= \frac 14\cos 80° + \frac 14[\cos(180°-80°) + \frac 12]\)
\(= \frac 14\cos 80° - \frac 14\cos80° + \frac 18\) \(\{\because \cos(180° - 80°) = - \cos80°\}\)
\(= \frac 18 \)
= RHS
