What is the value of \tan(\frac{3\pi}{8})?
- A. \sqrt{2}-1
- B. \sqrt{2}+1 ✓
- C. 1-\sqrt{2}
- D. -(\sqrt{2}+1)
Correct Answer: B. \sqrt{2}+1
Explanation
The angle \frac{3\pi}{8} = 67.5^{\circ}. We know that \tan(22.5^{\circ}) = \sqrt{2}-1. Thus, \tan(67.5^{\circ}) = \cot(22.5^{\circ}) = \frac{1}{\sqrt{2}-1} = \sqrt{2}+1.