43. Solve the inequality $4 \sin 3 \alpha+5 \geqslant 4 \cos 2 \alpha+5 \sin \alpha$.
43. The functions $\sin 3 \alpha$ and $\cos 2 \alpha$ expressed through the functions of the angle $\alpha$.

The inequality will take the form $(1-\sin \alpha)(4 \sin \alpha+1)^{2} \geqslant 0$.

We obtained an inequality that is valid for any $\alpha$.