Head shape and eye position and the long tail with shorter outer feathers makes this a definite Cooper's Hawk.
The problem is that the shape of the tail is often not definitive and can't be relied on.
Wheeler, at page 176 in the Eastern Edition of his RAPTORS of North America In the chapter on SIMILAR SPECIES to the Cooper's Hawk (which I quote in part) discusses the (1) Sharp-shinned Hawk, females -- "A long-standing identification dilemma for adults and juveniles when compared to male Cooper's Hawks. There is no overlap in size between the two species. Large female Sharp-shinned Hawks are considerably shorter in length and wingspan than male Cooper's Hawks. Numerous differences separate the two species. Proportional differences can separate them even when actual markings are not seen. PERCHED.-- Small, round shaped head at all times; however, Cooper's Hawks often compress their head feathers in warm temperatures so head also appears quite small. Yellow supraorbital ridge skin, if exposed, is apparent only at close range (often concealed by fluffed head feathers). Long thin tarsi. Rectrix length on underside of tail is helpful but use caution: females very round-tipped type tail with identical to Cooper's Hawks. (my underlining)
There is a corresponding paragraph to this in the Chapter on the Sharp-shinned Hawk at page 164 advising the use of caution "when comparing very rounded type of tail of female Sharp-shinned Hawks as they can be very like Cooper's Hawk. White terminal band on tail is wide in fall but may be mostly worn off by spring."
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