Question

cos 20°.cos40°.cos80°

Answer 1

Answer:

cos 20 cos 40 cos 80

= 2sin 20cos20 cos 40 cos 80/2sin20

= sin 40 cos 40 cos 80/2sin 20

= 2sin40cos40cos80/4sin20

= sin80cos80/4sin20

= 2sin80cos80/8sin20

= sin160/8sin20

= sin(180-20)/8sin20

Now, we know that sin(180-@) = sin @

So,

= sin(180-20)/8sin20

= sin20/8sin20

= 1/8

That is,

cos 20 cos 40 cos 80

= 1/8

Hope this helps you !