Question

prove that cos20 cos40 cos 60 cos80 =1/16

Answer 1

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cos20°cos40°cos60°cos80° = 1/16
1/2 [2cos20°cos40°]1/2 (cos80°)     *cos60° = 1/2
1/4 [cos (20°+40°)+cos (20°-40°)]cos80°
》2cosAcosB = cos (A+B)+cos (A-B) 《
1/4 [cos60°+cos20°]cos80°

》 Cos (-A ) = cosA 《
1/4 [1/2 + cos20°]cos80°
1/8cos80° + (1/4)(1/2)2cos20°cos80°
1/8cos80° + 1/8 [cos (20°+ 80°) + cos (20°- 80°)]
1/8cos80° + 1/8 [ cos100° + cos60° ]
1/8cos80° + 1/8cos100° + 1/8cos60°
1/8[ cos80° + cos100° ] + 1/8×1/2
1/8 [ cos80° + cos100° ] +1/16
1/8[{2cos(80°+100°)/2} {cos(80°-100°)/2}] + 1/16
1/8 [2cos90°] [cos20°/2] + 1/16
1/16
hence proved

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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!!!!!