Question

If for real values of $x,\cos\theta = x + \frac{1}{x},$ then

• A. $\theta$ is an acute angle
• B. $\theta$ is a right angle
• C. $\theta$is an obtuse angle
• D. No value of $\theta$is possible

Answer 1

Answer: (D)

No value of $\theta$is possible

Answer 2

The quadratic equation is $x^{2} - x\cos\theta + 1 = 0$

But x is real, therefore $B^{2} - 4AC \geq 0$

$\Rightarrow \cos^{2}\theta \geq 4(1)(1) \Rightarrow \cos^{2}\theta \geq 4$, which is impossible.