Answer: Using the multiple angle formula for cosine, we have:
cos 4x = 2cos^2 2x - 1
Now we need to rewrite cos 2x in terms of cos x. Again, using the multiple angle formula for cosine, we have:
cos 2x = 2cos^2 x - 1
Substituting this expression into the previous equation, we get:
cos 4x = 2(cos^2 x)^2 - 1
Simplifying the expression further, we have:
cos 4x = 2(cos^4 x) - 1
Therefore, cos 4x can be written in terms of cos x as 2(cos^4 x) - 1.
Explanation: