Question

Solution set of $\left[\right.sin^{- 1} x \left]\right. > \left[\right. cos^{- 1} ⁡ x \left]\right. ,$ where [.] denotes the greatest integer function, is

• A. $\left[\frac{1}{\sqrt{2}} , 1\right]$
• B. $\left(\right.cos 1 , \, sin ⁡ 1 \left.\right)$
• C. [ $sin \, 1, \, 1$ ]
• D. None of these

Answer 1

Answer: (C)

$\because\left[\sin ^{-1} x\right]>\left[\cos ^{-1} x\right]$ $\Rightarrow \quad x>0$
Here, $\left.[\cos ^{-1} x\right]=\left\{\begin{array}{ll}0, & x \in(\cos 1,1] \\ 1, & x \in(0, \cos 1]\end{array}\right. \\ \text { and }\left[\sin ^{-1} x\right]=\left\{\begin{array}{ll}0, & x \in(0, \sin 1) \\ 1, & x \in[\sin 1,1]\end{array}\right. \\ \therefore x \in[\sin 1,1]$