If \sec x=\frac{25}{24} and x lies in the fourth quadrant, then what is the value of \tan x+\sin x?
- A. -\frac{625}{168}
- B. -\frac{343}{600} ✓
- C. \frac{625}{168}
- D. \frac{343}{600}
Correct Answer: B. -\frac{343}{600}
Explanation
Since \sec x = \frac{25}{24}, we have \cos x = \frac{24}{25}. In the fourth quadrant, \sin x and \tan x are negative. Using the Pythagorean triplet (7, 24, 25), \sin x = -\frac{7}{25} and \tan x = -\frac{7}{24}. Then, \tan x + \sin x = -\frac{7}{24} - \frac{7}{25} = \frac{-175 - 168}{600} = -\frac{343}{600}.