Question

If A, B, C, D are the angles of a quadrilateral, then \[ \frac{\tan A + \tan B + \tan C + \tan D}{\cot A + \cot B + \cot C + \cot D} = \]

• A. \(\cot A\) \(\cot B\) \(\cot C\) \(\cot D\)
• B. \(\tan A\) \(\tan B\) \(\tan C\) \(\tan D\)
• C. \(
  \tan A\) \(\tan B\) \(\tan C\) \(\tan D\)
• D. \(
  \cot A\) \(\cot B\) \(\cot C\) \(\cot D\)

Hint:

For angles in a quadrilateral, the sum of angles is \( 360^\circ \). This property can be used to simplify trigonometric expressions involving the angles.