Determinant tactics-101

Algebra Level 5

\[\begin{vmatrix} \sin { ({ \alpha }+{ \alpha }_{ 1 }) } \sin { ({ \alpha - }{ \alpha }_{ 1 }) } & \quad \sin { ({ \alpha - }{ \alpha }_{ 1 }) } \cos { ({ \alpha + }{ \alpha }_{ 1 }) } & \quad 2\sin { ({ \alpha }) } \\ \sin { ({ \alpha + }{ \alpha }_{ 3 }) } \sin { ({ \alpha }-{ \alpha }_{ 3 }) } & \quad \sin { ({ \alpha -{ \alpha }_{ 3 } }) } \cos { ({ \alpha + }{ \alpha }_{ 3 }) } & \quad 2\sin { ({ \alpha }) } \\ \sin { ({ \alpha +{ \alpha }_{ 2 } }) } \sin { ({ \alpha - }{ \alpha }_{ 2 }) } & \quad \sin { ({ \alpha -{ \alpha }_{ 2 } }) } \cos { ({ \alpha }+{ \alpha }_{ 2 }) } & \quad 2\sin { ({ \alpha }) } \end{vmatrix}\]

Let the maximum value of this determinant be \(X\).

Find \(48X^{2}\).

This is part of my set Powers of the ordinary.
×

Problem Loading...

Note Loading...

Set Loading...