If =-1 2 and 0<x<2 , then the solutions are: - Vidyadip

MCQ

If $\cos\text{x}=-\frac{1}{2}$ and $0<\text{x}<2\pi,$ then the solutions are:

A
$\text{x}=\frac{\pi}{3},\ \frac{4\pi}{3}$
✓
$\text{x}=\frac{2\pi}{3},\ \frac{4\pi}{3}$
C
$\text{x}=\frac{2\pi}{3},\ \frac{7\pi}{3}$
D
$\theta=\frac{2\pi}{3},\ \frac{5\pi}{3}$

✓

Answer

Correct option: B.

$\text{x}=\frac{2\pi}{3},\ \frac{4\pi}{3}$

Given equation:
$\cos\text{x}=-\frac{1}{2}$
$\Rightarrow\cos\text{x}=\cos\frac{2\pi}{3}$
$\Rightarrow\text{x}=\frac{2\pi}{3}$
or
$\cos\text{x}=\cos\frac{4\pi}{3}$
$\Rightarrow\text{x}=\frac{4\pi}{3}$
so, both $\frac{2\pi}{3}$ and $\frac{4\pi}{3}$ line in $0<\text{}\text{x}<2\pi.$

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