Using principal value, evaluate the following: ^ -1 ( 2 3 )+ ^ -1… - Vidyadip

Question

Using principal value, evaluate the following:
$\cos^{-1}\Bigg(\cos\frac{2\pi}{3}\Bigg)+\sin^{-1}\Bigg(\sin\frac{2\pi}{3}\Bigg)$.

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Answer

$ \cos^{-1}\Big(\cos\frac{2\pi}{3}\Big)+\sin^{-1}\Big(\sin\frac{2\pi}{3}\Big)$
$=\frac{2\pi}{3}+\frac{2\pi}{3}=\frac{4\pi}{3}$.

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