Question:
Evaluate:
\[
\cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}}
\]
Evaluate:
\[
\cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}}
\]
Show Hint
Use standard values of inverse trigonometric functions for quick evaluation.
Updated On: Apr 2, 2025
- \( \pi \)
- \( \frac{\pi}{3} \)
- \( \frac{4\pi}{3} \)
- \( \frac{3\pi}{4} \)
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Evaluating inverse trigonometric values.
\[ \cos^{-1} \frac{1}{2} = \frac{\pi}{3}, \quad \sin^{-1} (1) = \frac{\pi}{2}, \quad \tan^{-1} \frac{1}{\sqrt{3}} = \frac{\pi}{6} \] Step 2: Summing up the values.
\[ \frac{\pi}{3} + \frac{\pi}{2} + \frac{\pi}{6} = \pi \]
\[ \cos^{-1} \frac{1}{2} = \frac{\pi}{3}, \quad \sin^{-1} (1) = \frac{\pi}{2}, \quad \tan^{-1} \frac{1}{\sqrt{3}} = \frac{\pi}{6} \] Step 2: Summing up the values.
\[ \frac{\pi}{3} + \frac{\pi}{2} + \frac{\pi}{6} = \pi \]
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