Evaluate

Engineering

Mathematics

Introduction to Determinants

Question

Evaluate $Δ = ∣ \begin{array}{cc} \cos 2 α & \sin 2 α \\ - \sin 3 α & \cos 3 α \end{array} ∣$

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Δ = ∣ \begin{array}{cc} \cos 2 α & \sin 2 α \\ - \sin 3 α & \cos 3 α \end{array} ∣

= cos⁡2α cos⁡3α + sin⁡3 αsin⁡2α

= cos⁡(2α – 3α)

= cos⁡(–α)

= cos⁡α

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