Question

\( \cot 12^\circ \times \cot 38^\circ \times \cot 52^\circ \times \cot 60^\circ \times \cot 78^\circ = \)?

• A. \( 1 \)
• B. \( \sqrt{3} \)
• C. \( \frac{1}{\sqrt{3}} \)
• D. \( 3 \)

Hint:

Using complementary angle identities: \( \cot (90^\circ - x) = \tan x \).

Answer 1

The Correct Option is C

Using trigonometric identities and symmetry properties:
\[ \cot 12^\circ \times \cot 78^\circ = 1, \] \[ \cot 38^\circ \times \cot 52^\circ = 1. \] Since \( \cot 60^\circ = \frac{1}{\sqrt{3}} \), the product simplifies to:
\[ 1 \times 1 \times \frac{1}{\sqrt{3}} = \frac{1}{\sqrt{3}}. \]