What is \cos 36^{\circ}-\cos 72^{\circ} equal to ?
- A. \frac{\sqrt{5}}{2}
- B. -\frac{\sqrt{5}}{2}
- C. \frac{1}{2} ✓
- D. -\frac{1}{2}
Correct Answer: C. \frac{1}{2}
Explanation
We know the standard values: \cos 36^{\circ} = \frac{\sqrt{5}+1}{4} and \cos 72^{\circ} = \frac{\sqrt{5}-1}{4}. Subtracting them gives \frac{\sqrt{5}+1}{4} - \frac{\sqrt{5}-1}{4} = \frac{2}{4} = \frac{1}{2}.