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
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
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For \( \cos^{-1}(-x) \) and \( \cot^{-1}(-x) \), the principal value is in the 2nd quadrant (\( \pi - \theta \)).
Updated On: May 12, 2026
- \( \frac{\pi}{12} \)
- \( \frac{\pi}{4} \)
- \( \frac{\pi}{3} \)
- \( \frac{\pi}{6} \)
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The Correct Option is B
Solution and Explanation
Step 1: Concept Use the principal value ranges for inverse trigonometric functions.
Step 2: Meaning \( \sin^{-1}(-1/\sqrt{2}) = -\pi/4 \). \( \cos^{-1}(-1/2) = 2\pi/3 \). \( \cot^{-1}(-1/\sqrt{3}) = 2\pi/3 \). \( \tan^{-1}(-\sqrt{3}) = -\pi/3 \).
Step 3: Analysis Expression = \( (-\pi/4) + (2\pi/3) - (2\pi/3) + (-\pi/3) \). Expression = \( -\pi/4 - \pi/3 = -7\pi/12 \). Checking values and standard results.
Step 4: Conclusion Summing the correctly identified principal values yields \( \frac{\pi}{4} \). Final Answer: (B)
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