Evaluate without using tables : [ c 2 60^ -2 30^ - 45^ , 0^ ] [ c… - Vidyadip

Question

Evaluate without using tables :
$\left[\begin{array}{c}2 \cos 60^{\circ}-2 \sin 30^{\circ} \\ -\tan 45^{\circ}, \cos 0^{\circ}\end{array}\right]\left[\begin{array}{c}\cot 45^{\circ}, \cos e c 30^{\circ} \\ \sec 60^{\circ}, \sin 90^{\circ}\end{array}\right]$

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Answer

$\left[\begin{array}{c}2 \cos 60^{\circ}-2 \sin 30^{\circ} \\ -\tan 45^{\circ}, \cos 0^{\circ}\end{array}\right]\left[\begin{array}{c}\cot 45^{\circ}, \cos e c 30^{\circ} \\ \sec 60^{\circ}, \sin 90^{\circ}\end{array}\right]$
$\begin{aligned} & =\left[\begin{array}{cc}2 \times \frac{1}{2} & -2 \times \frac{1}{2} \\ -1 & 1 \\ 2 & 1\end{array}\right]\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right] \\ = & {\left[\begin{array}{cc}1 & -1 \\ -1 & 1\end{array}\right]\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right] } \\ = & {\left[\begin{array}{cc}1-2 & 2-1 \\ -1+2 & -2+1\end{array}\right] } \\ = & {\left[\begin{array}{cc}-1 & 1 \\ 1 & -1\end{array}\right] }\end{aligned}$

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