Question

The value of \( \sin^{-1} \left( \frac{1}{\sqrt{5}} \right) + \cot^{-1}(3) \) is

• A. \( \frac{\pi}{6} \)
• B. \( \frac{\pi}{4} \)
• C. \( \frac{\pi}{3} \)
• D. \( \frac{\pi}{2} \)

Hint:

Use trigonometric identities to simplify inverse trigonometric expressions.

Answer 1

The Correct Option is A

To solve this, use the identity \( \sin^{-1} x + \cot^{-1} x = \frac{\pi}{2} \) to simplify the expression. By substituting the given values into the equation, the result is \( \frac{\pi}{6} \).
Step 2: Conclusion.
The correct answer is (A), \( \frac{\pi}{6} \).