cosA=1/2 than cos4A=?

4 answers

cos 4A
= cos^2 2A - sin^2 2A
= (cos 2A - sin 2A)(cos 2A + sin 2A)
= (cos^2 A - sin^2 A - 2sinAcosA)(cos^2 A - sin^2 A + 2sinAcosA)

from cosA = 1/2 ----> sinA = √3/2
(A = 60° or π/3)

plug the cos and sin values into my last equation and evaluate, I will leave the arithmetic up to you
cosA = 1/2
A = π/3
4A = 4π/3
cos4A = -1/2
Nice!!!

Well, I always like to take those long detours.
I once went from Toronto to Niagara Falls by going all the way around Lake Ontario.
As Crocodile Dundee would say,

Now that's a detour! (eh?)