Question

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

• A. \(\frac{\pi}{2} - \cot^{-1} x\)
• B. \(\frac{\pi}{2} - \sin^{-1} x\)
• C. \(\frac{\pi}{2} - \tan^{-1} x\)
• D. \(\frac{\pi}{2} - \sec^{-1} x\)

Hint:

Remember the identity \(\cos^{-1} x + \sin^{-1} x = \frac{\pi}{2}\) for \(x \in [-1,1]\).

Answer 1

The Correct Option is B

Step 1: Recall the complementary angle identity between inverse cosine and inverse sine: \[ \cos^{-1} x + \sin^{-1} x = \frac{\pi}{2} \] Step 2: Rearranging gives: \[ \cos^{-1} x = \frac{\pi}{2} - \sin^{-1} x \] ---