3.266. $\sin (x+2 \pi) \cos \left(2 x-\frac{7 \pi}{2}\right)+\sin \left(\frac{3 \pi}{2}-x\right) \sin \left(2 x-\frac{5 \pi}{2}\right)$.
## Solution.

$$
\begin{aligned}
& \sin (x+2 \pi) \cos \left(2 x-\frac{7 \pi}{2}\right)+\sin \left(\frac{3 \pi}{2}-x\right) \sin \left(2 x-\frac{5 \pi}{2}\right)= \\
& =\sin (2 \pi+x) \cos \left(\frac{7 \pi}{2}-2 x\right)+\sin \left(\frac{3 \pi}{2}-x\right)\left(-\sin \left(\frac{5 \pi}{2}-2 x\right)\right)= \\
& =\sin x(-\sin 2 x)+(-\cos x)(-\cos 2 x)=\cos 2 x \cos x-\sin 2 x \sin x=\cos 3 x
\end{aligned}
$$

Answer: $\cos 3 x$.