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
\(cos(4t) = cos(2(2t))\)
Now using the trignometric formula
\(cos2A = 2cos^{2}A - 1\)
\(cos2(2t) = 2(2cos^{2}t -1)^{2} -1\)
Apply (a +b )² = a² + b² + 2ab
\(cos2(2t) = 2(4cos^{4}t - 4cos^{2}t +1) -1\)
Simplify the above
\(cos2(2t) = 8cos^{4}t - 8cos^{2}t +1\)
Therefore the expression cos(4t) in terms of cos(t) is
\(cos2(2t) = 8cos^{4}t - 8cos^{2}t +1\)
