is his character devided or is it deliberate facade
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It is hard to tell whether he is using a facade; in either case he is disturbed because his "private" face is so sadistic and uncaring. If he is putting on a facade, he is a very serious conniver which, in itself, suggests disturbance.
Shakespeare doesn't portray an accurate description of the King, but he does apply the same disturbed facade to both hbis public and private persona.