Question

Спростити вираз: sin (pi/2-a) cos(2pi-a)+cos(3pi/2-a) sin(pi-a)

Answer 1

$\large \sin( \frac{\pi}{2} - \alpha ) \cdot \cos(2\pi - \alpha ) + \cos( \frac{3\pi}{2} - \alpha ) \cdot \sin(\pi - \alpha )$

$\large \cos \alpha \cdot \cos\alpha + ( - \sin\alpha ) \cdot \sin \alpha = \cos ^{2} \alpha - \sin ^{2} \alpha = \cos2 \alpha$