Question

If ${\left({\cos }^{-1}x\right)}^{2015}>{\left({\cos }^{-1}x\right)}^{2016}>{\left({\cos }^{-1}x\right)}^{2017}$ then $x$ lies in the interval

• A. $(\cos 2,\cos 1)$
• B. $(-1,0)$
• C. $(\cos 1,1)$
• D. $(0,\cos 1)$

Answer 1

Answer: (C)

$t={\cos }^{-1}x$
$t^{2015}>t^{2016}>t^{20117}$
$\therefore t\in (0,1)$
$0<{\cos }^{-1}x<1$
$\text{ and }\cos 1<x<1$