What is 1+\sin^{2}\left(\cos^{-1}\left(\frac{3}{\sqrt{17}}\right)\right) equal to?
- A. \frac{25}{17} ✓
- B. \frac{8}{17}
- C. \frac{9}{17}
- D. \frac{47}{17}
Correct Answer: A. \frac{25}{17}
Explanation
Let \theta = \cos^{-1}\left(\frac{3}{\sqrt{17}}\right), meaning \cos\theta = \frac{3}{\sqrt{17}}. Thus, \sin^2\theta = 1 - \cos^2\theta = 1 - \frac{9}{17} = \frac{8}{17}. The full expression is 1 + \sin^2\theta = 1 + \frac{8}{17} = \frac{25}{17}.