Consider the following statements:<br>1. \sin \theta = x + \frac{1}{x} is possible for some real value of x.<br>2. \cos \theta = x + \frac{1}{x} is possible for some real value of x.<br>Which of the above statements is/are correct?
- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2 ✓
Correct Answer: D. Neither 1 nor 2
Explanation
For any real x \neq 0, the magnitude |x + \frac{1}{x}| \geq 2. However, the range of both \sin \theta and \cos \theta is [-1, 1]. Therefore, neither equation is possible for any real value of x.
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