Question

\( \tan^{-1} \sqrt{3} - \sec^{-1}(-2) \) is equal to:

• A. \( \pi \)
• B. \( \frac{\pi}{3} \)
• C. \( \frac{\pi}{3} \)
• D. \( \frac{2\pi}{3} \)

Hint:

For inverse trigonometric functions, remember the values of common angles like \( \frac{\pi}{3}, \frac{\pi}{6}, \) and \( \frac{\pi}{4} \) for sine, cosine, and tangent.

Answer 1

The Correct Option is C

Step 1: Using inverse trigonometric identities.
We know that \( \tan^{-1} \sqrt{3} = \frac{\pi}{3} \) and \( \sec^{-1}(-2) = \frac{2\pi}{3} \), so: \[ \tan^{-1} \sqrt{3} - \sec^{-1}(-2) = \frac{\pi}{3} - \frac{2\pi}{3} = -\frac{\pi}{3} \]

Step 2: Conclusion.
Thus, the correct value is \( \frac{\pi}{3} \), which corresponds to option (3).