Question

Prove that cos20 cos40° cos60° cos80° = 1/16 

Answer 1

we multiply the ques with 2*sin20
now
2sinx* cosx=sin2x
so
lhs=(2*sin20*cos20)*cos40*cos60*cos80/2sin20
     =(sin40*2*cos40)*cos60*cos80/4sin20
     =(sin80*c0s80*2)*cos60/8sin20
     =sin160/16sin20                                                                    (cos60=1/2)
     =sin(180-20)/16sin20
    =sin20/16sin20
   =1/16
so
lhs=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!!!!!