Question

1/2 cos20. Cos40. Cos80

Answer 1

Multiply by 2 sin 20 and divide by it 

cos 20.cos 40.cos 80 = 2 sin 20 cos 20.cos 40.cos 80 / 2 sin 20 

now 2 sin 20 cos 20 = sin 40 so we have 

= sin 40 cos 40 cos 80 / 2 sin 20 
multiply by 2 and divide by 2 
= 2 sin 40 cos 40 cos 80 / 4 sin 20 

= sin 80 cos 80/ 4 sin 20 

= 2 sin 80 cos 80 /8 sin 20 

= sin 160 / 8 sin 20 

= sin ( 180 -20) / 8 sin 20 = sin 20/8 sin 20 

= 1/8

so 1/2*1/8=1/16