What is \frac{\cos 17^{\circ}-\sin 17^{\circ}}{\cos 17^{\circ}+\sin 17^{\circ}} equal to?
- A. \tan 34^{\circ}
- B. \cot 34^{\circ}
- C. \tan 62^{\circ}
- D. \cot 62^{\circ} ✓
Correct Answer: D. \cot 62^{\circ}
Explanation
Dividing the numerator and the denominator by \cos 17^{\circ}, the expression transforms to \frac{1 - \tan 17^{\circ}}{1 + \tan 17^{\circ}}. This matches the expansion formula for \tan(45^{\circ} - \theta), giving \tan(45^{\circ} - 17^{\circ}) = \tan 28^{\circ}. Since \tan 28^{\circ} = \cot(90^{\circ} - 28^{\circ}) = \cot 62^{\circ}, the expression is equal to \cot 62^{\circ}.