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For example, in my DSP book, these transfer functions are given:

H1(z) = (z+b)/(z+a) 0<|a|<1

H2(z) = (bz+1)/(z+a) 0<|b|<1

It then goes on to calculate the arg without showing any steps:

arg[H1(e^jw)] = arctan(sin w/(b+cos w)) - arctan(sin w/(a+cos w))

and

arg[H2(e^jw)] = arctan(b*sin w/(1+b*cos w)) - arctan(sin w/(a+cos w))

Could anyone explain to me how this is calculated?

Thanks.