If x + frac{1}{x} = 2 cos theta, then x^3 + f | vedclass

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

Question

(B) Given $x + \frac{1}{x} = 2 \cos 	heta$. We know the algebraic identity $a^3 + b^3 = (a + b)^3 - 3ab(a + b)$. Substituting $a = x$ and $b = \frac{

Vedclass · Accepted Answer

$2 \cos 3	heta$

Vedclass · Answer

(B) Given $x + \frac{1}{x} = 2 \cos 	heta$. We know the algebraic identity $a^3 + b^3 = (a + b)^3 - 3ab(a + b)$. Substituting $a = x$ and $b = \frac{1}{x}$,we get: $x^3 + \frac{1}{x^3} = \left(x + \frac{1}{x}ight)^3 - 3 \left(x \cdot \frac{1}{x}ight) \left(x + \frac{1}{x}ight)$ $= (2 \cos 	heta)^3 - 3(1)(2 \cos 	heta)$ $= 8 \cos^3 	heta - 6 \cos 	heta$ $= 2(4 \cos^3 	heta - 3 \cos 	heta)$ Using the trigonometric identity $\cos 3	heta = 4 \cos^3 	heta - 3 \cos 	heta$,we get: $= 2 \cos 3	heta$.

If $x + \frac{1}{x} = 2 \cos \theta,$ then $x^3 + \frac{1}{x^3} = $

Similar Questions

For the value of $\frac{2 \tan(x)}{1-\tan^2(x)}$ to be positive,find the values of $x$ such that $x \in \left(0, \frac{\pi}{2}\right)$.

Evaluate: $\cos \frac{\pi}{5} \cos \frac{2\pi}{5} \cos \frac{4\pi}{5} \cos \frac{8\pi}{5}$

If $\tan \theta = \frac{1}{3}$,then $\cos 2 \theta = $

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 -

If $\tan x = \frac{3}{4}$ and $\pi < x < \frac{3\pi}{2}$,find the values of $\sin \frac{x}{2}$,$\cos \frac{x}{2}$,and $\tan \frac{x}{2}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module