If x is real and x+frac{1}{x}=2 cos theta, th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given the equation $x+\frac{1}{x}=2 \cos 	heta$.Multiplying by $x$,we get $x^2 - 2x \cos 	heta + 1 = 0$.Since $x$ is a real number,the discrimin

Vedclass · Accepted Answer

$\pm 1$

Vedclass · Answer

(C) Given the equation $x+\frac{1}{x}=2 \cos 	heta$.Multiplying by $x$,we get $x^2 - 2x \cos 	heta + 1 = 0$.Since $x$ is a real number,the discriminant $D$ of this quadratic equation must be greater than or equal to $0$.$D = b^2 - 4ac = (-2 \cos 	heta)^2 - 4(1)(1) = 4 \cos^2 	heta - 4$.Setting $D \geq 0$,we have $4 \cos^2 	heta - 4 \geq 0$,which implies $\cos^2 	heta \geq 1$.Since the range of $\cos 	heta$ is $[-1, 1]$,the only possible values satisfying $\cos^2 	heta \geq 1$ are $\cos 	heta = 1$ or $\cos 	heta = -1$.Thus,$\cos 	heta = \pm 1$.

If $x$ is real and $x+\frac{1}{x}=2 \cos \theta,$ then $\cos \theta=$

Similar Questions

The value of $\cot \frac{\pi}{20} \cot \frac{3 \pi}{20} \cot \frac{5 \pi}{20} \cot \frac{7 \pi}{20} \cot \frac{9 \pi}{20}$ is

If $x = \sec \theta + \tan \theta ,$ then $x + \frac{1}{x} = $

The value of $\tan 1^{\circ} \tan 2^{\circ} \ldots \tan 89^{\circ}$ is

If $x = \sec \phi - \tan \phi$ and $y = \csc \phi + \cot \phi$,then which of the following is true?

If $\frac{\sec 8\theta - 1}{\sec 4\theta - 1} = \frac{a + b\tan^2 2\theta}{1 + c\tan^2 2\theta + d\tan^4 2\theta}$ (where $\theta \neq \frac{n\pi}{16}, n \in I$),then the value of $(a - b + c - d)$ is -

Vedclass Test Series

Exam Paper Generator

Online Exam Module