Question

Упростить выражение cos(3п+а) * sin(п - а) - sin2( п/2 + а)​

Answer 1

$\cos(3\pi+\alpha )\cdot \sin (\pi-\alpha )-\sin^2\left(\dfrac{\pi}2+\alpha \right)=\\\\=\cos(\pi+\alpha )\cdot \sin (\pi-\alpha )-\bigg(\sin\left(\dfrac{\pi}2+\alpha \right)\bigg)^2=\\\\=-\cos\alpha\cdot \sin \alpha-\left(\cos\alpha \right)^2=\\\\\boldsymbol{=-\cos\alpha (\sin\alpha +\cos\alpha )}$