2cos ( a - П/3) - 2sin ( П/3 + а )

Question

2cos ( a - П/3) - 2sin ( П/3 + а )

Answer 1

2cosa*cosП/3+2sinasinП/3-2sinп/3cosa-2sinacosП/3=(2*1/2)cosa+(2√3/2)sina-(2√3/2)cosa-2*1/2*sina=cosa+√3sina-√3cosa-sina=√3(sina-cosa)-(sina-cosa)=(sina-cosa)(√3-1)