Solution:

L.H.S = cos20cos40cos60cos80

= cos20cos40$\frac{1}{2}$cos80

= $\frac{1}{4}$(2cos20cos40)cos80

= $\frac{1}{4}$(cos60 + cos20)cos80

= $\frac{1}{4}\big(\frac{1}{2} + Cos20\big)Cos80$

= $\frac{1}{4}\big(\frac{1}{2}Cos80 + Cos20Cos80\big)$

= $\frac{1}{8}(Cos80 + 2Cos20Cos80)$

= $\frac{1}{8}$(Cos80 + Cos100 + Cos60)

= $\frac{1}{8}\big(Cos80 + Cos100 + \frac{1}{2}\big)$

= $\frac{1}{4}\big(Cos80 + Cos(\pi - 80) + \frac{1}{2}\big)$

= $\frac{1}{8}\big(Cos80 - Cos80 + \frac{1}{2} \big)$

= $\frac{1}{16}$

R.H.S