The difference of the maximum and the minimum values of the function  5 cosx+3  cos(x+π3)+8  over R is

5cosx+3cosx2−32sinx+8=  132cosx−332sinx+8Whose minimum and maximum values are              8−1322+3322     and      8+1322+3322=1    and     15∴Maximum – minimum = 15 – 1 = 14