MCQ
The principal solution of $\cos ^{-1}\left(-\frac{1}{2}\right)$ is :
- A$\frac{\pi}{3}$
- B$\frac{\pi}{6}$
- C$\frac{2 \pi}{3}$
- D$\frac{3 \pi}{2}$
The principal solution of $\cos ^{-1}\left(-\frac{1}{2}\right)=$ An angle in $[0, \pi]$, whose cosine is $-1 / 2$
$\Rightarrow \cos ^{-1}\left(-\frac{1}{2}\right)=\pi-\cos ^{-1}\left(\frac{1}{2}\right) \quad \ldots \ldots\left[\right.$ [because $\left.\cos ^{-1}(-x)=\pi-\cos x\right]$
$=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}$
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