l [ cc 2 30^ & -2 60^ - 45^ & 90^ ] [ cc 45^ & 60^ cosec 30^ & 0^… - Vidyadip

Question

$\begin{array}{l}{\left[\begin{array}{cc}2 \sin 30^{\circ} & -2 \cos 60^{\circ} \\ -\cot 45^{\circ} & \sin 90^{\circ}\end{array}\right]} {\left[\begin{array}{cc}\tan 45^{\circ} & \sec 60^{\circ} \\ \operatorname{cosec} 30^{\circ} & \cos 0^{\circ}\end{array}\right]}\end{array}$

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Answer

$\begin{array}{l}{\left[\begin{array}{cc}2 \sin 30^{\circ} & -2 \cos 60^{\circ} \\ -\cot 45^{\circ} & \sin 90^{\circ}\end{array}\right]} \\\end{array} $
$ {\left[\begin{array}{rr}\tan 45^{\circ} & \sec 60^{\circ} \\ \operatorname{cosec} 30^{\circ} & \cos 0^{\circ}\end{array}\right]} $
$ =\left[\begin{array}{cc}2 \times \frac{1}{2}-2 \times \frac{1}{2}\end{array}\right]\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right] $
$=\left[\begin{array}{cc}1 & 1 \\ -1 & 1\end{array}\right]\left[\begin{array}{cc}1 & 2 \\ 2 & 1\end{array}\right]$
$=\left[\begin{array}{cc}-1 & 1 \\ 1 & -1\end{array}\right]$

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