The set of values of `x` satisfying `|sin^(- 1)x|lt|cos^(- 1)x|,`is

Options

A. `[-1,1/sqrt2]`
B. `[-1,-1/sqrt2] uu [1/sqrt2,1]`
C. `(-1,1/sqrt2)`
D. `[1/sqrt2,1]` only

Answer

To solve the inequality \( |\sin^{-1} x| < |\cos^{-1} x| \), we will follow these steps:

### Step 1: Understand the ranges of the inverse trigonometric functions
The function \( \sin^{-1} x \) (arcsine) is defined for \( x \) in the range \([-1, 1]\) and takes values in \([- \frac{\pi}{2}, \frac{\pi}{2}]\). The function \( \cos^{-1} x \) (arccosine) is also defined for \( x \) in the range \([-1, 1]\) and takes values in \([0, \pi]\).