If ​ cos x=

Question:

If $\cos x=-\frac{1}{2}$ and $0

(a) $x=\frac{\pi}{3}, \frac{4 \pi}{3}$

(b) $x=\frac{2 \pi}{3}, \frac{4 \pi}{3}$

(c) $x=\frac{2 \pi}{3}, \frac{7 \pi}{6}$

(d) $\theta=\frac{2 \pi}{3}, \frac{5 \pi}{3}$

Solution:

(b) $x=\frac{2 \pi}{3}, \frac{4 \pi}{3}$

Given equation:

$\cos x=-\frac{1}{2}$

$\Rightarrow \cos x=\cos \frac{2 \pi}{3}$

$\Rightarrow x=\frac{2 \pi}{2}$

Or,

$\cos x=\cos \frac{4 \pi}{3}$

$\Rightarrow x=\frac{4 \pi}{3}$

So, both $\frac{2 \pi}{3}$ and $\frac{4 \pi}{3}$ lie in $0

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