Consider the following statements in respect of the determinant \(\left| {\begin{array}{*{20}{c}} {{{\cos }^2}\frac{\alpha }{2}}&{{{\sin }^2}\frac{\alpha }{2}}\\ {{{\sin }^2}\frac{\beta }{2}}&{{{\cos }^2}\frac{\beta }{2}} \end{array}} \right|\)Where α, β are complementary angles1. The value of the determinant is \(\frac{1}{{√ 2 }}\cos \left( {\frac{{\alpha - \beta }}{2}} \right)\;\)2. The maximum value of the determinant is \(\frac{1}{\sqrt2}\)Which of the above statements is/are correct?

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2