sin(x + 2π) = (sin x)(cos ) + (cos x)(sin 2π) = (sin x)( ) + (cos x)(0)

Explanation:

Step1: Recall the angle - addition formula for sine

The formula for $\sin(A + B)=\sin A\cos B+\cos A\sin B$. Here $A = x$ and $B = 2\pi$, so the first blank is $2\pi$.

Step2: Evaluate $\cos(2\pi)$

We know that the cosine function has a period of $2\pi$, and $\cos(2k\pi)=1$ for any integer $k$. When $k = 1$, $\cos(2\pi)=1$, so the second blank is $1$.

Answer:

First blank: $2\pi$; Second blank: $1$