Evaluate Δ=∣0sin⁡α−cos⁡α−sin⁡α0sin⁡βcos⁡α−sin⁡β0∣.\text{Evaluate } \Delta = \begin{vmatrix} 0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0 \end{vmatrix}.

Mathematics

Problem

Evaluate Δ=∣0sin⁡α−cos⁡α−sin⁡α0sin⁡βcos⁡α−sin⁡β0∣.\text{Evaluate } \Delta = \begin{vmatrix} 0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0 \end{vmatrix}.

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