Question

The value of \( \sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) + \cos^{-1\left(-\frac{1}{2}\right) - \cot^{-1}\left(-\frac{1}{\sqrt{3}}\right) + \tan^{-1}(-\sqrt{3}) \) is

• A. \( \frac{\pi}{12} \)
• B. \( \frac{\pi}{4} \)
• C. \( \frac{\pi}{3} \)
• D. \( \frac{\pi}{6} \)

Hint:

For \( \cos^{-1}(-x) \) and \( \cot^{-1}(-x) \), the principal value is in the 2nd quadrant (\( \pi - \theta \)).

Answer 1

The Correct Option is B