If k is a root of x^{2}-4x+1=0, then what is \tan^{-1}k+\tan^{-1}\frac{1}{k} equal to?
- A. -\pi/2
- B. 0
- C. \pi/4
- D. \pi/2 ✓
Correct Answer: D. \pi/2
Explanation
Since the product of the roots is 1 and the sum is 4, both roots are positive. For any k \gt 0, \tan^{-1}(1/k) = \cot^{-1}k. Therefore, \tan^{-1}k + \cot^{-1}k = \pi/2.