A) a > b > d > c
B) d > c > a > b
C) b > a > d > c
D) a < b < d < c
Correct Answer: B
Solution :
When \[x\,\in \,(0,1)\] \[\Rightarrow \] \[{{\cos }^{-1}}\,x>{{\sin }^{-1}}\,x\] Also, \[{{\cos }^{-1}}x>1\] and \[{{\sin }^{-1}}\,x<1\] \[\therefore \] \[{{({{\cos }^{-1}}x)}^{{{\cos }^{-1}}x}}\] is greatest and \[({{\sin }^{-1}}x)\] least. \[\Rightarrow \] \[{{({{\sin }^{-1}})}^{{{\sin }^{-1}}x}}<\,{{({{\cos }^{-1}}x)}^{{{\sin }^{-1}}x}}\] \[\Rightarrow \] \[d>c>a>b\]You need to login to perform this action.
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