Solution set of [.sin- 1 x ]. [. cos- 1 ⁡ x ]. , where [.] denotes the greatest integer function, is

Question

Solution set of [.sin- 1 x ]. > [. cos- 1 ⁡ x ]. , where [.] denotes the greatest integer function, is (A) [(1/√2) , 1] (B) (.cos 1 , sin ⁡ 1 .) (C) [ sin 1, 1 ] (D) None of these

Tardigrade Admin · Accepted Answer

∵[ sin -1 x]>[ cos -1 x] ⇒ x>0 Here, .[ cos -1 x]= beginarrayll0, x ∈( cos 1,1] 1, x ∈(0, cos 1] endarray. text and [ sin -1 x]= beginarrayll0, x ∈(0, sin 1) 1, x ∈[ sin 1,1] endarray. ∴ x ∈[ sin 1,1]

Q. Solution set of $[s i n^{- 1} x] > [co s^{- 1} x],$ where [.] denotes the greatest integer function, is

$[\frac{1}{2}, 1]$

$(cos 1, s in 1)$

[ $s in 1, 1$ ]

None of these

$∵ [sin^{- 1} x] > [cos^{- 1} x]$ $\Rightarrow x > 0$
Here, $[cos^{- 1} x] = {0, 1, x \in (cos 1, 1] x \in (0, cos 1] and [sin^{- 1} x] = {0, 1, x \in (0, sin 1) x \in [sin 1, 1] ∴ x \in [sin 1, 1]$

Q. Solution set of [sin−1x]>[cos−1⁡x], where [.] denotes the greatest integer function, is

[2​1​,1]

(cos1,sin⁡1)

[ sin1,1 ]