Answer
Find out the cos(4t) in terms of cos(t) .
To prove
As given the identity in the question be cos(4t) .
It is written as
[tex]cos(4t) = cos(2(2t))[/tex]
Now using the trignometric formula
[tex]cos2A = 2cos^{2}A - 1[/tex]
[tex]cos2(2t) = 2(2cos^{2}t -1)^{2} -1[/tex]
Apply (a +b )² = a² + b² + 2ab
[tex]cos2(2t) = 2(4cos^{4}t - 4cos^{2}t +1) -1 [/tex]
Simplify the above
[tex]cos2(2t) = 8cos^{4}t - 8cos^{2}t +1 [/tex]
Therefore the expression cos(4t) in terms of cos(t) is
[tex]cos2(2t) = 8cos^{4}t - 8cos^{2}t +1 [/tex]
