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

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

Question

(D) Given $2 \cos 	heta = x + \frac{1}{x}$,which implies $\cos 	heta = \frac{1}{2} \left(x + \frac{1}{x}ight)$.Using the triple angle identity $\c

Vedclass · Accepted Answer

$x^3 + \frac{1}{x^3}$

Vedclass · Answer

(D) Given $2 \cos 	heta = x + \frac{1}{x}$,which implies $\cos 	heta = \frac{1}{2} \left(x + \frac{1}{x}ight)$.Using the triple angle identity $\cos 3 	heta = 4 \cos^3 	heta - 3 \cos 	heta$,we have:$2 \cos 3 	heta = 2 [4 \cos^3 	heta - 3 \cos 	heta] = 8 \cos^3 	heta - 6 \cos 	heta$.Substitute $\cos 	heta = \frac{1}{2} \left(x + \frac{1}{x}ight)$:$2 \cos 3 	heta = 8 \left[ \frac{1}{2} \left(x + \frac{1}{x}ight) ight]^3 - 6 \left[ \frac{1}{2} \left(x + \frac{1}{x}ight) ight]$$= 8 \left[ \frac{1}{8} \left(x^3 + \frac{1}{x^3} + 3(x + \frac{1}{x}) ight) ight] - 3 \left(x + \frac{1}{x}ight)$$= \left(x^3 + \frac{1}{x^3} + 3(x + \frac{1}{x}) ight) - 3 \left(x + \frac{1}{x}ight)$$= x^3 + \frac{1}{x^3}$.

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

Similar Questions

If $\cos \theta = \frac{1}{2}\left( a + \frac{1}{a} \right),$ then the value of $\cos 3\theta$ is

$\tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A = $

$\tan 3A - \tan 2A - \tan A = $

If $\sec x + \tan x = 2$,where $0 < x < \frac{\pi}{2}$,then find the value of $\sin \frac{x}{4}$.

If $\frac{\tan 3A}{\tan A} = a$,then $\frac{\sin 3A}{\sin A}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module