Prove that cos 20° cos 40° cos 60° cos 80° = 3/16

Question

Prove that cos 20° cos 40° cos 60° cos 80° = \(\frac{3}{16}\)

Answer 1

LHS = cos 20° cos 40° cos 60° cos 80°

= cos 20° cos 40° (\(\frac{1}{2}\)) cos 80° [∵ cos 60° = \(\frac{1}{2}\)]

= \(\frac{1}{2}\)(cos 20° cos 40° cos 80°)

= \(\frac{1}{2}\)(\(\frac{2sin20°}{2sin20°}\)) (cos 20° cos 40° cos 80°)

[multiply and divide by 2 sin 20°]

[multiply and divide by 2]

Hence Proved.