If \( x = \sec \theta - \tan \theta \) and \( y = \operatorname{cosec} \theta + \cot \theta \), then which one of the following is correct ?
- A. x + y - xy - 1 = 0
- B. x - y + xy + 1 = 0 ✓
- C. x + y + xy - 1 = 0
- D. x - y + xy - 1 = 0
Correct Answer: B. x - y + xy + 1 = 0
Explanation
Substituting a test angle like \theta = 45^\circ yields x = \sqrt{2} - 1 and y = \sqrt{2} + 1. Checking the options with these values satisfies the equation x - y + xy + 1 = 0.