Question

For real \(x\), if \(x+\frac{1}{x}=2\cos\theta\), then \(\cos\theta\) is

• A. \(\pm 1\)
• B. \(\frac{1}{2}\)
• C. \(1\)
• D. \(\pm\frac{1}{2}\)

Hint:

For real \(x\), \(x+\frac{1}{x}\) cannot lie between \(-2\) and \(2\), except at the end values. Since \(2\cos\theta\) lies between \(-2\) and \(2\), only \(\pm2\) are possible.

Answer 1

The Correct Option is A