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Ans: (A)  \( \frac{1}{\sqrt2}<x\leq\:1\)

 

Because when \(x\in\:\big(\frac{1}{\sqrt2}.1\big],\:\:\:sin^{-1}x\:\in\:\big(\frac{\pi}{4},\frac{\pi}{2}\big]\)

and    \(cos^{-1}x\:\in\:\big[0,\frac{\pi}{4}\big)\)

\(\Rightarrow\:sin^{-1}x\:is\:>\:cos^{-1}x\:\)  in this interval.
answered Mar 17, 2013 by rvidyagovindarajan_1
 
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