Question

Prove that cos20*cos40*cos60*cos80=1/6

Answer 1

cos20cos40cos60cos80=1/6
multiply both sides by sin20
sin20cos20cos40cos60cos80=asin20
By double angle formula,
#sin20cos20=1/2sin40
We can continue this pattern.
1/2sin40cos40cos60cos80=asin20
1/4sin80cos80cos60=asin20
1/8sin160cos60=asin20
cos60 is simply 1/2
So,
1/16sin160=asin20
However,
sin160=sin20
So, a=1/16

Answer 2

DEAR STUDENT,

Kindly check the attached papers for a detailed solution along with step by step elaboration to reach our final solution that is our final desired or required answer to this query that is completely proved.

$\boxed{\bf{\underline{L.H.S. = R.H.S.}}}$

Which is the required proof or solution process for this type of query.

Hope this helps you and solves your doubts for applying trigonometric identifies to reach a proper solution or a proof!!!!!