Question

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

Answer 1

cos 20 *  cos40  *cos 60  *cos  80 =  (1/2) cos 20  *cos 40  *cos 80 =
(1/2) 1/2(cos 120+cos 40) *  cos 20 = (1/4) cos 20* (-1/2 + cos 40)
= (-1/8) cos 20 + (1/4) cos 20 * cos 40 = 
(-1/8) cos 20 + (1/4)(1/2)(cos 60 + cos 20) =
(-1/8) cos 20 + (1/8) cos 60 + (1/8) cos 20   = (1/8)(1/2) = 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!!!!!