Question

Find an identity for cos(4t) in terms of cos(t)?

Answer 1

The question in the problem wants to calculate the identity for  cos(4t) in terms of cos(t) and base on the given and further computation, I would say that the answer would be 2cos^2(2t)-1. I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarification

Answer 2

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

$cos2(2t) = 8cos^{4}t - 8cos^{2}t +1$