Question

If \( k \leq \sin^{-1} x + \cos^{-1} x + \tan^{-1} x \leq 5 \), then:

• A. \( k = 0, K = \pi \)
• B. \( k = 0, K = \frac{\pi}{2} \)
• C. \( k = 0, K = \frac{\pi}{2} \)
• D. None of these

Hint:

Trigonometric identities can simplify expressions for sums of inverse functions.

Answer 1

The Correct Option is B

Step 1: Use trigonometric identities.
By using the known trigonometric identities, we calculate the possible values of \( k \) and \( K \), which are 0 and \( \frac{\pi}{2} \) respectively.
Thus, the correct answer is (2).