Question

Evaluate: \[ \cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}} \]

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

Hint:

Use standard values of inverse trigonometric functions for quick evaluation.

Answer 1

The Correct Option is A

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.
\[ \frac{\pi}{3} + \frac{\pi}{2} + \frac{\pi}{6} = \pi \]