Consider the following statements:<br>I. (\text{cosec } \alpha-\sec \alpha) is <strong>ALWAYS</strong> positive in the first quadrant.<br>II. (\tan \alpha-\cot \alpha) is <strong>ALWAYS</strong> negative in the first quadrant.<br>Which of the statements given above is/are correct?
- A. I only
- B. II only
- C. Both I and II
- D. Neither I nor II ✓
Correct Answer: D. Neither I nor II
Explanation
For \alpha = 60^\circ, \text{cosec } 60^\circ \approx 1.15 and \sec 60^\circ = 2, making it negative. Also \tan 60^\circ - \cot 60^\circ = \sqrt{3} - 1/\sqrt{3} which is positive. Both statements are false.
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