- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
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
Solution
(d) The quadratic equation is ${x^2} – x\cos \theta + 1 = 0$
But $x$ is real, therefore ${B^2} – 4AC \ge 0$
$ \Rightarrow {\cos ^2}\theta \ge 4(1)(1) \Rightarrow {\cos ^2}\theta \ge 4$, which is impossible.
Standard 11
Mathematics
