Solve $\sin ^{-1}\left(x^2-2 x+1\right)+\cos ^{-1}\left(x^2-x\right)=\frac{\pi}{2}$
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Solve $\sin ^{-1}\left(x^2-2 x+1\right)+\cos ^{-1}\left(x^2-x\right)=\frac{\pi}{2}$

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SOLUTION : $\sin ^{-1}(f(x))+\cos ^{-1}(g(x))=\frac{\pi}{2}  \Leftrightarrow  f(x)=g(x) \text { and }-1 \leq f(x), g(x) \leq 1 \\$

$x^2-2 x+1=x^2-x  \Leftrightarrow  x=1, \text { accepted as a solution }$

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