Question

8cos20°.cos40°.cos80°=1​

Answer 1

Correct.

Explanation:

I am assuming you want to verify the above. If you enter this product into your calculator you'll get a result of 1.

Answer 2

see explanation

Explanation:

Using the double angle identity

sin2x = 2sinxcosx

Consider the left side

cos20. cos40. cos80

=
`(1)/(2sin20)` (2sin20cos20)cos40.cos80

=
`(1)/(2sin20)` (sin40cos40cos80

=
`(1)/(4sin20)` (2sin40cos40)cos80

=
`(1)/(4sin20)` (sin80cos80)

=
`(1)/(8sin20)` (2sin80cos80)

=
`(1)/(8sin20)` sin160

=
`(1)/(8sin20)` sin(180 - 20)

=
`(1)/(8sin20)` sin20

=
`(1)/(8)`

Hence

8(cos20cos40cos80) = 8 ×
`(1)/(8)` = 1 = right side