Question

If \( x \in [-1,1] \), then \(\displaystyle \sin^{-1}(-x) = \)

• A. \(-\sin^{-1} x\)
• B. \(\sin^{-1} x\)
• C. \(-\cos^{-1} x\)
• D. \(\cos^{-1} x\)

Hint:

Inverse sine is an odd function: \(\sin^{-1}(-x) = -\sin^{-1} x\).

Answer 1

The Correct Option is A

Step 1: Using the odd function property of \(\sin^{-1} x\): \[ \sin^{-1}(-x) = -\sin^{-1} x \] for all \(x \in [-1,1]\). ---