Question

Prove that cos20cos40cos60cos80 = 1/16

Answer 1

Hey there !!!!!!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

=cos20cos40cos60cos80 

Multiply and divide with 2sin20 

=2sin20cos20cos40cos60cos80/2sin20

We know that 2sinAcosA = sin 2A

So 2sin20cos20 = sin2*20 =sin40

= sin40cos40cos60cos80/2sin20

Multiply and divide with "2"

= 2sin40cos40cos60cos80/2*2sin20

=cos60sin80cos80/2*2sin20

Multiply and divide with "2"

= cos60*2sin80cos80/8sin20

= cos60sin160/8sin20

We know that 

sin(180-∅) = sin∅

So sin160 = sin(180-20) = sin20

So,

= cos60sin160/8sin20

=cos60sin20/8sin20

= cos60/8

cos60 = 1/2

= 1/16

LHS = RHS

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope this helped you...............

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!!!!!