1.
Consider the following statements in respect of the determinant
∣cos⁡2(α/2)sin⁡2(α/2)sin⁡2(β/2)cos⁡2(β/2)∣\begin{vmatrix} \cos^2(\alpha/2) & \sin^2(\alpha/2) \\ \sin^2(\beta/2) & \cos^2(\beta/2) \end{vmatrix}

where α,β\alpha, \beta are complementary angles.

1. The value of the determinant is 12cos⁡α−β2\frac{1}{\sqrt{2}} \cos\frac{\alpha-\beta}{2}.
2. The maximum value of the determinant is 12\frac{1}{\sqrt{2}}.

Which of the above statements is/are correct?