Final answer:
To rewrite cos(x + 65π) using sinx and cosx, we see that it simplifies to cosx without the need of any additional rewriting due to the periodic nature of cosine, where 65π is an integer multiple of 2π, a full cycle.
Step-by-step explanation:
To rewrite cos(x + 65π) using sinx and cosx, we need to apply trigonometric identities. Since 65π is an integer multiple of 2π, it constitutes a full cycle or multiple cycles around the unit circle, which means that cos(x + 65π) = cosx. No further rewriting is necessary since cosx is already in terms of cosx. However, if we had to express cos(x+65π) using sinx, we could use the trigonometric identity cos(\u03b1 ± \u03b2) = cos \u03b1 cos \u03b2 sin \u03b1 sin \u03b2 from line 11 of the reference. After simplifying, we would still end with cosx because of the periodic nature of cosine function.