Question

PROVE THAT COS 20 DEGREE COS 40 DEGREE COS 60 DEGREE COS 80 DEGREE =1/16

Answer 1

Hi

cos20°cos40°cos60°cos80°
=(1/2)(2cos20°cos40°)(1/2)cos80°
[*:,cos60°=1/2]
=(1/4)[cos(20°+40°)+cos(20°-40°)]cos80°
=(1/4)(cos60°+cos20°)cos80°
=(1/4)(cos60°cos80°+cos20°cos80°)
=(1/4)(1/2)cos80°+(1/4)cos20°cos80° =(1/8)cos80°+(1/4)(1/2)(2cos20°cos80°) =(1/8)cos80°+(1/8)[cos(20°+80°) +cos(20°-80°)]
=(1/8)cos80°+(1/8)(cos100°+cos60°)
=(1/8)cos80°+(1/8)cos100°+(1/8)cos60°
=(1/8)(cos80°+cos100°)+(118)x(112)
=(1/8)[{2cos(80°+100°)/2)[cos(80°-100°)/ 2)]+(1/16)
=(1/8)(2cos90°cos10°)+(1/16)
=0+(1/16) [cos90°=0]
=1/16 (proved)

♡I hope u got ur answer♡

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!!!!!