Question

Prove that cos20 cos40 cos60 cos80=1/16

Answer 1

sin20.sin40.cos60.cos80 = (1/2)[2 sin20.sin40.cos60.cos80]
= (1/2){[cos 20 + cos 60]cos60.cos80}
= (1/2){[cos 20 + (1/2)](1/2).cos80}
= (1/8){[2cos 20 + 1].cos80}
= (1/8)[2cos 20 cos80 + cos80]
= (1/8)[cos 100 + cos60 + cos80]
= (1/8)[- cos 80 + (1/2) + cos80]
= (1/8) (1/2) = (1/16)
= RHS

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!!!!!