Question:
Mark the tick against the correct answer in the following:
The principal value of $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ is
A. $\frac{\pi}{6}$
B. $\frac{5 \pi}{6}$
C. $\frac{7 \pi}{6}$
D. none of these
Solution:
To Find:The Principle value of $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
Let the principle value be given by $\mathrm{x}$
Now, let $x=\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
$\Rightarrow \cos x=\frac{\sqrt{3}}{2}$
$\Rightarrow \cos x=\cos \left(\frac{\pi}{6}\right)\left(\because \cos \left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}\right)$
$\Rightarrow \mathrm{x}=\frac{\pi}{6}$
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