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$α = \sin^{- 1} (\cos (\sin^{- 1} x))$ and $β = \cos^{- 1} (\sin (\cos^{- 1} x)),$ then

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$\tan α = - \cot β$

$\tan α = - \tan β$

$\tan α = \cot β$

$\tan α = \tan β$

answer is A.

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Detailed Solution

$β = \cos^{- 1} (\cos (\frac{π}{2} - \cos^{- 1} x)); β = \cos^{- 1} {\cos (\sin^{- 1} x)}$
also $α = \sin^{- 1} [\cos (\sin^{- 1} x)]$
$α + β = π / 2 \Rightarrow \tan α = \cot β$

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