Question

Find the value of cos20cos40cos60cos80

Answer 1

hi friend,

given,let c= cos20cos40cos60cos80

let us consider s=sin20sin40sin60sin80


c×s=cos20sin20cos40sin40cos60sin60cos80sin80


multiply and divide with 16

c×s=(2sin20cos20)(2cos40sin40)(2sin60cos60)(2sin80cos80)/16


c×s=sin40sin80sin120sin160/16


c×s=sin40sin80sin(180-60)sin(180-20)/16



c×s=sin40sin80sin20sin60/16




we know that sin20sin40sin60sin80=s



so, we get




c×s=s/16



dividing with s on both sides ,we get




c=1/16


where c=cos20cos40cos60cos80





I hope this will help u;)

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!!!!!