If A = frac{1}{pi} begin{bmatrix} sin^{-1}(xp | vedclass

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(D) Given matrices are $A = \begin{bmatrix} \frac{1}{\pi} \sin^{-1}(x\pi) & \frac{1}{\pi} 	an^{-1}(\frac{x}{\pi}) \ \frac{1}{\pi} \sin^{-1}(\frac{x}

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$\frac{1}{2}I$

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(D) Given matrices are $A = \begin{bmatrix} \frac{1}{\pi} \sin^{-1}(x\pi) & \frac{1}{\pi} 	an^{-1}(\frac{x}{\pi}) \ \frac{1}{\pi} \sin^{-1}(\frac{x}{\pi}) & \frac{1}{\pi} \cot^{-1}(\pi x) \end{bmatrix}$ and $B = \begin{bmatrix} -\frac{1}{\pi} \cos^{-1}(x\pi) & \frac{1}{\pi} 	an^{-1}(\frac{x}{\pi}) \ \frac{1}{\pi} \sin^{-1}(\frac{x}{\pi}) & -\frac{1}{\pi} 	an^{-1}(\pi x) \end{bmatrix}$.Subtracting $B$ from $A$:$A-B = \begin{bmatrix} \frac{1}{\pi}(\sin^{-1}(x\pi) + \cos^{-1}(x\pi)) & \frac{1}{\pi}(	an^{-1}(\frac{x}{\pi}) - 	an^{-1}(\frac{x}{\pi})) \ \frac{1}{\pi}(\sin^{-1}(\frac{x}{\pi}) - \sin^{-1}(\frac{x}{\pi})) & \frac{1}{\pi}(\cot^{-1}(\pi x) + 	an^{-1}(\pi x)) \end{bmatrix}$.Using the identities $\sin^{-1}(	heta) + \cos^{-1}(	heta) = \frac{\pi}{2}$ and $	an^{-1}(	heta) + \cot^{-1}(	heta) = \frac{\pi}{2}$,we get:$A-B = \begin{bmatrix} \frac{1}{\pi} \cdot \frac{\pi}{2} & 0 \ 0 & \frac{1}{\pi} \cdot \frac{\pi}{2} \end{bmatrix} = \begin{bmatrix} \frac{1}{2} & 0 \ 0 & \frac{1}{2} \end{bmatrix} = \frac{1}{2} I$.

Factory	Men and Women Workers
$I$	$30$ Men,$25$ Women
$II$	$25$ Men,$31$ Women
$III$	$27$ Men,$26$ Women

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