Q. 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
Explanation
(d)
The quadratic equation is $x^{2} - x\cos{\theta + 1 = 0}$
Since, $x$ is real, therefore discriminant $\geq 0$
$\Rightarrow B^{2}4\ AC \geq 0\ \Rightarrow \cos^{2}{\theta \geq 4(1)(1) \Rightarrow \cos^{2}{\theta \geq 4}}$
Which is impossible because $\cos^{2}\theta\$is not greater than 1
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.