Rewrite the expression so that it involves the sum or difference of only constants and sines and cosine to the 1st power

(cos 5x)^2

To rewrite the expression (cos 5x)^2 in terms of only constants, sines, and cosines to the 1st power, we can use the trigonometric identity:

(cos θ)^2 = 1/2 * (1 + cos 2θ)

In this case, let's substitute θ with 5x:

(cos 5x)^2 = 1/2 * (1 + cos 2(5x))

Now simplify the expression:

(cos 5x)^2 = 1/2 * (1 + cos 10x)

Therefore, (cos 5x)^2 can be rewritten as 1/2 * (1 + cos 10x), involving only constants, sines, and cosines to the 1st power.