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

Let f(x)=5cosx+3cos(x+60°)+8=5cosx+3(cosxcos60°−sinxsin60°)+8=132cosx−332sinx+8This is of the form acosx+bsinx+c,where a=132,b=−332,c=8We have a2+b2=7The extreme values of f over R arec±a2+b2=8±7=15,1‘15’ is the max value and ‘1' is the min value of the function f over R