If \tan^{-1}k+\tan^{-1}\frac{1}{2}=\frac{\pi}{4}, then what is the value of k?
- A. 1
- B. 1/2
- C. 1/3 ✓
- D. 1/4
Correct Answer: C. 1/3
Explanation
\tan^{-1}k = \frac{\pi}{4} - \tan^{-1}\frac{1}{2}. Taking tan on both sides gives k = \frac{\tan(\pi/4) - 1/2}{1 + \tan(\pi/4)(1/2)} = \frac{1 - 1/2}{1 + 1/2} = 1/3.