Cos(2П/3-a)-cos(a+П/3)

cos(2П / 3 - a) - cos(a + П / 3) =

= cos(2П / 3) * cos(a) + sin(2П / 3) * sin(a) - (cos(a) * cos(П / 3) - sin(a) * sin(П / 3)) =

= (-1 / 2) * cos(a) + √3 / 2 * sin(a) - (cos(a) * 1 / 2 - sin(a) * √3/2) =

= (-cos(a)) / 2 + (√3 * sin(a)) / 2 - (cos(a) / 2 - (√3 * sin(a)) / 2) =

= (-cos(a)) / 2 + (√3 * sin(a)) / 2- (cos(a) - √3 * sin(a)) / 2 =

= (-cos(a) + √3 * sin(a) - (cos(a) - √3 * sin(a))) / 2 =

= (-cos(a) + √3 * sin(a) - cos(a) + √3 * sin(a)) / 2 =

= (-2cos(a) + 2√3 * sin(a)) / 2 =

= 2(-cos(a)) + √3 * sin(a)) / 2 =

= -cos(a) + √3 * sin(a)

Ответ : -cos(a) + √3 * sin(a)