Evaluate :

Engineering

Mathematics

Introduction to Determinants

Question

Evaluate : $∣ \begin{array}{cc} \cos 30^{\circ} & \sin 30^{\circ} \\ \sin 105^{\circ} & \cos 105^{\circ} \end{array} ∣$

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∣ \begin{array}{cc} \cos 30^{\circ} & \sin 30^{\circ} \\ \sin 105^{\circ} & \cos 105^{\circ} \end{array} ∣

= cos⁡30º cos⁡105º – sin⁡30º sin⁡105º

= cos⁡30º + 105º using cos⁡A cos⁡B – sin⁡A sin⁡B = cos⁡(A + B)

= cos⁡135º = cos⁡90º + 45º

$= - \sin 45^{\circ} = - \frac{1}{\sqrt{2}}$

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