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# If $A=\begin{bmatrix}2 & sec^{-1}x\\-1 & cosec^{-1} x \end{bmatrix}$ is a singular matrix then find the value of $x$

$\begin{array}{1 1} 0 \\ -1 \\ 1 \\ \sqrt 2\end{array}$

Toolbox:
• If a matrix is singular then its determinant is zero.
• $cosec^{-1}x+sec^{-1}x=\large\frac{\pi}{2}$
Given: $A=\begin{bmatrix}2 & sec^{-1}x\\-1 & cosec^{-1} x \end{bmatrix}$ is a singular matrix
$\Rightarrow\:|A|=2cosec^{-1}x+sec^{-1}x=0$
$\Rightarrow\:cosec^{-1}x+cosec^{-1}x+sec^{-1}x=0$
We know that $cosec^{-1}x+sec^{-1}x=\large\frac{\pi}{2}$