A) \[{{a}^{2}}\]
B) \[{{b}^{2}}\]
C) \[{{c}^{2}}\]
D) None of these
Correct Answer: C
Solution :
\[(a-b){{\cos }^{2}}\frac{C}{2}+{{(a+b)}^{2}}{{\sin }^{2}}\frac{C}{2}\] \[=({{a}^{2}}+{{b}^{2}}-2ab){{\cos }^{2}}\frac{C}{2}\] \[+({{a}^{2}}+{{b}^{2}}+2ab){{\sin }^{2}}\frac{C}{2}\] \[={{a}^{2}}+{{b}^{2}}+2ab\left( {{\sin }^{2}}\frac{C}{2}-{{\cos }^{2}}\frac{C}{2} \right)\] \[={{a}^{2}}+{{b}^{2}}-2ab\cos C\] \[={{a}^{2}}+{{b}^{2}}-({{a}^{2}}+{{b}^{2}}-{{c}^{2}})\] \[={{c}^{2}}\]
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