Question

Prove that cos20cos40cos60cos80 = 1/16

Answer 1

cos20 cos40 cos60 cos80= 1/16 l.h.s. : cos20 cos40 1/2 cos80 (cos60 = 1/2) multiply nd divide by 2 1/4 (2 cos20 cos40 cos80) 1/4 (cos(20+80)+ cos(20-80)) cos40 (2cosa cosb= cos(a+b) + cos(a-b)) 1/4 (cos(-60)+ cos(100)) cos40 1/4(1/2 + cos100)cos40 1/8 cos40+ 1/4 (cos40 cos100) multiplt nd divide by 2 2/2(1/8 cos40) + 1/8(2 cos40 cos100) 1/8 cos40+ 1/8 (cos140+ cos(-60)) (2cosa cosb= cos(a+b) cos(a-b)) 1/8 cos40+ 1/8 cos140 + 1/16 (cos60= 1/2) 1/8(cos40+cos140) + 1/16 1/8(2 cos90 cos(-50)) + 1/16 (as above identity) cos90= 0 1/16 = r.h.s

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!!!!!