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 angles
1. 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?1
1 only
2
2 only
3
Both 1 and 2
4
Neither 1 nor 2