Question

If \( \cos \cot^{-1} \left( \frac{1}{2} \right) = \cot (\cos^{-1} x) \), then the value of \( x \) is:

• A. \( \frac{1}{\sqrt{6}} \)
• B. \( \frac{-1}{\sqrt{12}} \)
• C. \( \frac{2}{\sqrt{6}} \)
• D. \( \frac{-2}{\sqrt{6}} \)

Hint:

To convert inverse trigonometric expressions, use the basic definitions of trigonometric functions in right-angled triangles.