Question

Prove that cos 20 cos 40 cos 60 cos 80 is equal to 1/16

Answer 1

Hii....

here is your answer...

cos20°.cos40°.cos60°.cos80° = 1/16

Solution => Taking L.H.S ,

= (cos20°.cos40°)cos60°.cos80°

= 1/2 [cos(20° + 40°) + cos(20° – 40°)]×1/2×cos80°

= 1/4 [cos60° + cos(-20°)]cos80°

= 1/4 [cos60°cos80° + cos20°cos80°]

= 1/4 [1/2cos80° + 1/2{cos(20° + 80°) + cos(20° – 80°)}]

= 1/8 [cos80° + {cos100° + cos(-60°)}]

= 1/8 [cos80° + cos100° + cos60°]

= 1/8 [cos80° +cos(180° – 80°) +cos60°]

= 1/8 [cos80° – cos80° + cos60°]

= 1/8 ×cos60°

= 1/8 × 1/2

= 1/16 = R.H.S

Therefore , L.H.S = R.H.S
Hence , proved

( Following identities are used in the above question )
◆ cos(-A) = cosA
◆ cosA.cosB = 1/2 [cos(A + B) + cos(A – B) ]
◆ cos60° = 1/2

hope this helps :)

thank 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!!!!!