Question

Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

• A. \(-\frac{\pi}{2}\)
• B. \(-\frac{\pi}{4}\)
• C. \(\frac{\pi}{4}\)
• D. \(\frac{\pi}{2}\)

Hint:

Remember the negative signs for inverse trigonometric identities: - \(\sec^{-1}(-x) = \pi - \sec^{-1}(x)\) - \(\csc^{-1}(-x) = -\csc^{-1}(x)\) Converting everything immediately into terms of \(\sin^{-1}\) and \(\cos^{-1}\) minimizes memory slip-ups.

Answer 1

The Correct Option is B