LITHIUM-COBALT BASED COMPLEX OXIDE HAVING SUPERIOR LIFESPAN CHARACTERISTICS AND CATHODE ACTIVE MATERIAL FOR SECONDARY BATTERIES INCLUDING THE SAME The present invention relates to a lithium-cobalt based complex oxide having superior lifespan characteristics and a cathode active material for secondary batteries including the same. More pal-titularly, the present invention relates to a lithium-cobalt based complex oxide including lithium and cobalt maintaining a crystal structure of a 10 single 03 phase at a state of charge (SOC) of 50% or more. As mobile device technology continues to develop and demand therefor continues to increase, denland for secondary batteries as energy sources is rapidly increasing. Among these secondary batteries, lithium secondary batteries, which have 15 high energy density and operating voltage, long cycle lifespan, and low self-discharge rate, are commercially available and widely used. In addition, recently, lithium ion batteries are commercially used as a power supply in home electronics such as laptop computers, mobile phones and the like. -1- Furtherniore, as interest in environmental problcms is increasing, research into electric vehicles (EVs), hybrid electric vehicles (I-IEVs), and the like that can replace vehicles using fossil fuels, such as gasoline vehicles, diesel vehicles, and the like, which are one of the main causes of air pollution, is underway. 5 As a cathode of conventionally used lithium ion batteries, lithium cobalt oxides such as LiCo02 having a layered structure are used. As an anode, graphite based materials are generally used. Lithium cobalt oxides are currently widely used due to superior physical properties such as superior cycle characteristics as compared to LiNiOz and LiMnz04. 10 To develop seconhy batteries having high energy density, cathode active materials having large capacity are required. However, when operating voltage of lithium cobalt oxides are fixed unlike thee component-based cathode active materials, it is substantially impossible to enlarge capacities of materials. Accordingly, lithium cobalt oxides must be used under high voltage to develop 15 secondary batteries having high energy density. However, approximately 50% or more of lithium ions are eliminated under high voltage operation, structures of lithium cobalt oxides collapse and, as such, lifespan characteristics are rapidly degraded. To overcome this problem and to achieve high energy density, technologies substituting some cobalt with Al, ,Mg, B or the like, or treating surfaces of lithium cobalt oxides with a metal oxide such as A1203, MgzO, Ti02 or the like are !mown. Howevel; when some cobalt is substituted with metals described above, there 5 is still a problem such as degradation of lifespan characteristics. When a surface of a lithium cobalt oxide is coated with a metal oxide, specific capacity may be reduced due to addition of a coating material that does not directly participate in charge and discharge reaction, and a metal oxide with vely low electrical conductivity mainly constitutes the coating material, which results in reduced conductivity. In addition, the 10 coating process reduces active reaction area, thereby increasing interfacial resistance and deteriorating high-rate charge and discharge characteristics. Therefore, there is an urgent need to develop technology for fundamentally addressing these problems and enhancing high voltage lifespan characteristics of a lithium cobalt oxide. 15 [DISCLOSURE] The present invention aims to address the aforementioned problen~s of the related art and to achieve technical goals that have long been sougl~t. As a result of a variety of intensive studies and various experiments, the inventors of the present invention confirmned that rate characteristics and lifespan characteristics are inlproved when a lithium-cobalt based comnplex oxide maintains a crystal structure of a single 03 phase at a state of charge (SOC) of 50% or more, 5 namely, under high voltage, thus colnpleting the present invention. In accordance with one aspect of the present invention, provided is a lithiumcobalt based complex oxide including lithium, cobalt and manganese, represented by Formula 1 below, wherein the lithium-cobalt based complex oxide maintains a crystal 10 structure of a single 03 phase at a state of charge (SOC) of 50% or nlore based on a theoretical amount: wherein 0.951x11.15,O Lithium-cobalt based complex oxide samples manufactured according to Examples 1 and 4, and Comparative Example 1 were prepared. An X-ray diffraction 10 (XRD) pattern of each sample was collected using a Siemens D500 diffiactometer equipped with copper target X-ray tube and diffsacted beam monochromator. Since the samples are thick and wide, the samples were manufactured in a flat and rectangular powder-bed shape such that volume irradiated by X-ray beat11 is constant. Using GSAS of a Rietveld refinement program disclosed in [A. C. Larson and R. B. Von Dreele, 15 "General Stmcture Analysis System (GSAS)", Los Alamos National Laboratory Report LAUR 86-748 (2000)], a lattice constant of a unit cell was calculated. Results are sutnmarized in Table 1 below. Here, crystal structures of unit cells tnanufactnred according to Example 1 and Comparative Example 1 were nleasured in a full voltage range. The lithium-cobalt base& complex oxide sa~nple manufactured according to Example 4 maintained a crystal structure of a single 03 phase in voltage of 4.4 V or more.A crystal structure was not measured below the voltage range. 5 Referring to Table 1, the lithiutn-cobalt based oxides manufactured according to Examples 1 and 4 maintained crystal structures of single 03 phases under full charging voltage not exceeding 4.50 V. On the other hand, the lithium-cobalt based complex oxide manufactured according to Comparative Example 1 showed another phase, in addition to an 03 phase, over 4.35 V, resulting in two phases. Subsequently, at 10 4.50 V, all 03 phases transitioned to the another phase, resulting in formation of one phase. Using each of the lithium-cobalt based conlplex oxides manufactured according to Exanlple 1 to 3 and Cotnparative Exanlple 1, the lithium-cobalt based conlplex oxide:a conductive material (Denka b1ack):a binder (PVdF) in a weight ratio of 95:2.5:2.5 were added to NMP and then mixed to manufacture a cathode mixture. The 5 cathode mixture was coated to a thickriess of 200 Vrn on an aluminum foil and then pressed and dried. As a result, a cathode was manufactured. To manufacture a lithium secondary battery, Li metal was used as an anode and a carbonate based electrolyte, namely, 1 ~nol LiPF6 dissolved in a mixture of ethyl carbonate (EC) and ethyl methyl carbonate (EMC) mixed in a ratio of 1:l was used as 10 an electrolyte. Measurement of initial charge and discharge capacities, and eficieticies When the lnanufactured lithium secondary batteries were charged and discharged at 0.1 C in a voltage range of 3.0 V to 4.4 V, initial capacities and efficiencies wvere measured. Results are summarized in Table 2 below. Measurement of lifespan characteristics After charging and discharging the manufactured lithium secondary batteries once at 0.1 C in chambers of 250 and in a voltage range of 3.0 V to 4.4 V, lifespan characteristics wvere measured fifty times while charging at 0.5 C and discharging at 1 C. After charging and discharging once at 0.1 C in a 450 chamber and in a voltage -21- range of 3.0 V to 4.5 V, lifespan characteristics were measured fifty tillles while charging at 0.5 C and discharging at 1 C. Results are su~nnlarizedi n Table 2 below and illustrated in FIGS. 1 to 10. Measurement of rate characteristics 5 Rate characteristics of the manufactured lithium secondary batteries were tested in a voltage range of 3.0 V to 4.4 V and capacity at each C-rate with I-espect to capacities at 0.1 C was calculated. Results are summarized in Table 2 below and illustrated in FIG. 11. [Table 21 Example 1 Example 2 Example 3 Comparative Example 1 Initial capacity and efficiency Lifespan characteristics Rate characteristics (YOa,t 50 cycles) 1.0 C 98.0 98.4 99.2 93.9 Charge (mAh/g) 180.5 180.3 179.6 180.9 Discharge (tnAldg) 177.4 177.1 176 176.8 Efficiency (%) 98.2 98.3 98.0 97.8 Referring to Table 2 and FIGS. 1 to 10, initial capacities and efficiencies of lithium secondary batteries using the lithium-cobalt based complex oxides nlanufaetured according to Examples 1 to 3 were sliglitly higher but were not greatly different, when compared to those of a lithiu~n secondary battery using the lithium- 5 cobalt based conlplex oxide manufactnred according to Comparative Example 1. However, rate characteristics and lifespan characteristics of the lithium secondary batteries using the lithium-cobalt based complex oxides manufactured according to Examples 1 to 3 were superior, when compared to those of a lithium secondary battery using the lithium-cobalt based complex oxide manufactured according to Comparative 10 Example 1. In particular, rate characteristics at a high rate and lifespan characteristics at high tenlperature werevastly*superior. As described in Experimental Example 1, the lithium-cobalt based complex oxide manufactured according to Example 1 maintained the crystal stn~cture of the single 0 3 phase even under high voltage. On the other hand, the 0 3 phase of the 15 lithium-cobalt based complex oxide manufactured according to Conlparative Example 1 is partially or entirely changed into the P3 phase and thereby charge and discharge are not maintained and irreversible capacity increases. For reference, in FIGS. 1 and 2, graphs of Exatnple 2 overlap with graphs of Example 3 and thereby the graphs are not easily distinguished. Using each of the lithium-cobalt based complex oxides manufactured according to Examples 1, 6 and 7, the lithium-cobalt based conlplex oxide:a conductive material (Denka b1ack):a binder (PVdF) in a weight ratio of 95:2.5:2.5 were added to 5 NMP and then mixed to manufacture a cathode mixture. The cathode mixtme was coated to a thickness of 200 pm on an aluminum foil and then pressed and dried. As a result, a cathode was manufactured. To manufacture a lithium secondary battery, Li metal was used as an anode and a carbonate based electrolyte, namely, 1 mol LiPF6 dissolved in a mixture of ethyl 10 carbonate (EC) and ... ethyl methyl carbonate (EMC) mixed in a ratio of 1:l was used as an electrolyte. After charging and discharging the manufactured lithium secondary batteries once at 0.1 C in a 450 chamber and in a voltage range of 3.0 V to 4.5 V, lifespan characteristics were measured fifty times while charging at 0.5 C and discharging at 1 15 C. Results are illustrated in FIG. 12. Referring to FIG. 12, the lithium-cobalt based complex oxides, which are doped with Mg, manufactured according to Examples 6 and 7 sl~owede xcellent lifespan characteristics, when compared with the lithium-cobalt based conlplex oxide manufactured according to Exalnple 1. Those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed it1 the accompanying claims. 5 As described above, a lithium-cobalt based complex oxide according to the present invention maintains a c~ystals tructure of a single 03 phase at a state of charge (SOC) of 50% or more, namely, under high voltage and thereby collapse of a sttvcture of the lithium-cobalt based complex oxide is prevented, and, accordingly, rate characteristics and lifespan characteristics are improved. [claim 11 A lithium-cobalt based colnplex oxide represented by Forlnula 1 below comprising lithium, cobalt and manganese, wherein the lithium-cobalt based colnplex oxide lnailitains a crystal structure of a single 03 phase at a state of charge 5 (SOC) of 50% or more based on theoretical capacity: wherein 0.955~51.15,O