2020 · Q49
Consider the following statements:
- 1sin θ = x + 1/x is possible for some real value of x.
- 2cos θ = x + 1/x is possible for some real value of x.
Which of the above statements is/are correct?
Elementary MathematicsTrigonometry
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
For real x, |x+1/x| >= 2, whereas |sin(theta)| and |cos(theta)| are at most 1. Neither statement is possible - option (D). The minimum of |x+1/x| is 2 (attained at x = +-1), already exceeding the sine/cosine range of [-1, 1].