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Show that the equation sin(theta) = x + 1/x cannot hold for any real x. Which statement is correct?

1. No real x satisfies it, since |x + 1/x| >= 2 > 1.
2. It holds for all x in (0,1).
3. It holds only when x = 1.
4. It holds for every real x not equal to 0.

Correct answer: No real x satisfies it, since |x + 1/x| >= 2 > 1.

Solution

For any nonzero real x, |x + 1/x| >= 2, while |sin theta| <= 1, so equality is impossible.

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