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.