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The value of the determinant $\left|\begin{array}{rr}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|$ is : |
$a$ $a^2$ 1 $2 a$ |
$a^2$ |
$\left|\begin{array}{rr}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|$ $=(a \cos \theta)(a \cos \theta)-(-a \sin \theta)(a \sin \theta)$ $=a^2 \cos ^2 \theta+a^2 \sin ^2 \theta$ $\Delta=a^2\left(\sin ^2 \theta+\cos ^2 \theta\right)$ as $\sin ^2 \theta+\cos ^2 \theta = 1$ $=a^2$ |
