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( begin{aligned} lim _{x rightarrow 1}(1-x) tan frac{pi}{2} x &=lim _{x rightarrow 1} frac{1-x}{cot frac{pi}{2} x} &=lim _{x rightarrow 1} frac{-1}{-operatorname{cosec}^{2}left(frac{pi}{2} xright) cdot frac{2}{pi}}(L text { Horpimes }) &=frac{operatorname{lt}left(frac{pi}{x-1}right) frac{2 sin ^{2}left(frac{pi}{2} xright)}{pi}}{frac{2}{pi}} end{aligned} )

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