19.11. 1) sin3x · cos3x = 0,5; 2) cos²2x − sin²2x = −√3/2; 3) sin2x · cos2x = −1/2; 4) sin²3x − cos²3x = −1/2.

По обводке — № 19.11.

1. \(\sin3x\cos3x=\frac12\sin6x=\frac12\Rightarrow \sin6x=1\Rightarrow x=\frac{\pi}{12}+\frac{\pi k}{3}\);

2. \(\cos^2 2x-\sin^2 2x=\cos4x=-\frac{\sqrt3}{2}\Rightarrow x=\pm\frac{5\pi}{24}+\frac{\pi k}{2}\);

3. \(\sin2x\cos2x=\frac12\sin4x=-\frac12\Rightarrow \sin4x=-1\Rightarrow x=-\frac{\pi}{8}+\frac{\pi k}{2}\);

4. \(\sin^2 3x-\cos^2 3x=-\cos6x=-\frac12\Rightarrow \cos6x=\frac12\Rightarrow x=\pm\frac{\pi}{18}+\frac{\pi k}{3}\).

\(k\in\mathbb Z\).