∫cos(x−a)cos(x−b)  dx=

∫cos(x−b+b−a)cos(x−b) dx  =∫cos(x−b)cos(b−a)−sin(x−b)sin(b−a)cos(x−b) dx =∫cos(b−a) dx-sin(b−a)∫tanx-b dx=xcos(b−a)−sin(b−a)log|sec(x−b)|+C