If (2cos x - 1)(3 + 2cos x) = 0 for 0 le x le | vedclass

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

Question

(B) Given the equation $(2\cos x - 1)(3 + 2\cos x) = 0$. This implies either $2\cos x - 1 = 0$ or $3 + 2\cos x = 0$. Case $1$: $2\cos x - 1 = 0 \Right

Vedclass · Accepted Answer

$\frac{\pi}{3}, \frac{5\pi}{3}$

Vedclass · Answer

(B) Given the equation $(2\cos x - 1)(3 + 2\cos x) = 0$. This implies either $2\cos x - 1 = 0$ or $3 + 2\cos x = 0$. Case $1$: $2\cos x - 1 = 0 \Rightarrow \cos x = \frac{1}{2}$. For $0 \le x \le 2\pi$,the solutions are $x = \frac{\pi}{3}$ and $x = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}$. Case $2$: $3 + 2\cos x = 0 \Rightarrow \cos x = -\frac{3}{2}$. Since the range of $\cos x$ is $[-1, 1]$,the equation $\cos x = -\frac{3}{2}$ has no real solution. Thus,the values of $x$ in the interval $[0, 2\pi]$ are $\frac{\pi}{3}$ and $\frac{5\pi}{3}$.

If $(2\cos x - 1)(3 + 2\cos x) = 0$ for $0 \le x \le 2\pi$,then $x = $

Similar Questions

The smallest positive angle which satisfies the equation $2\sin^2 \theta + \sqrt{3} \cos \theta + 1 = 0$ is

The general solution of $2 \sqrt{3} \cos^2 \theta = \sin \theta$ is

If $2\sin \theta + \tan \theta = 0$,then the general values of $\theta$ are

The general solution of the trigonometric equation $(\sqrt{3}-1) \sin \theta + (\sqrt{3}+1) \cos \theta = 2$ is

The number of solutions of the given equation $a \sin x + b \cos x = c$,where $|c| > \sqrt{a^2 + b^2}$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module