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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

Solution set of [ ^ -1 x ] > [ ^ -1 x ] , where [.] denotes the...

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

Options

  1. A[12,1]\left[\dfrac{1}{\sqrt{2}}, 1\right]
  2. B(cos⁡1,sin⁡1)( \cos 1,\sin 1 )
  3. C[\sin 1, 1]]
  4. DNone of these

Correct answer

C. [\sin 1, 1]]

Step-by-step solution

∵ [ \sin^{- 1} x ] > [ \cos^{- 1} x ]<br/><br/><br /><br />⇒ x > 0<br /><br />Here, \left[\cos^{- 1}x\right] = \left\{\begin{cases}0, & x \in ( \cos 1, 1 ] \\ 1, & x \in ( 0, \cos 1 ]\end{cases}\right)<br /><br />and\left[\sin^{- 1}x\right] = \left\{{0,x∈(0,sin⁡1)1,x∈[sin⁡1,1]\begin{cases}0, & x \in ( 0, \sin 1 ) \\ 1, & x \in [ \sin 1, 1 ]\end{cases}\right)

∴x∈[sin⁡1,1]∴ x \in [ \sin 1, 1 ]
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