Question

prove that cos20cos40cos60cos80 =1/16

Answer 1

cos20°cos40°cos60°cos80°
=(1/2sin20°)(2sin20°cos20°)cos40°cos60°cos80°
=(1/2sin20°)sin40°cos40°cos60°cos80° [∵, 2sinAcosA=sin2A]
=(1/4sin20°)(2sin40°cos40°)cos60°cos80°
=(1/4sin20°)sin80°cos80°cos60°
=(1/8sin20°)(2sin80°cos80°)(1/2)
=(1/16sin20°)sin160°
=(1/16sin20°)sin{(90°×2)-20°}
=(1/16sin20°)sin20°
=1/16 (Proved)

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!!!!!