Use double angle formula for cosine:
[tex]cos (2a) = 2cos^2(a) - 1[/tex]
Apply to cos(4t)
[tex]cos (2(2t)) = 2 cos^2 (2t) - 1 \\ cos (2t) = 2 cos^2 t - 1[/tex]
Sub 2nd equation into 1st equation:
[tex]cos(4t) = 2 (2 cos^2 t -1)^2 - 1 \\ = 8 cos^4 t -8cos^2 t +1[/tex]
