Question

Спростити вираз: 2sin(pi/6-a)+cos(pi+a)+√3sina

Answer 1

$2\sin(\frac{\pi}{6}-a)+\cos(\pi+a)+\sqrt{3}\sin a=2(\sin\frac{\pi}{6}\cos a-\cos\frac{\pi}{6}\sin a)-\cos a+\sqrt{3}\sin a=2(\frac{1}{2}\cos a-\frac{\sqrt{3}}{2}\sin a)-\cos a+\sqrt{3}\sin a=2(\frac{\cos a}{2}-\frac{\sqrt{3}\sin a}{2})-\cos a+\sqrt{3}\sin a=2\frac{\cos a-\sqrt{3}\sin a}{2}-\cos a+\sqrt{3}\sin a=\cos a-\sqrt{3}\sin a-\cos a+\sqrt{3}\sin a=0$