Write the principal value

Question:

Write the principal value of $\cos ^{-1}\left(\cos 680^{\circ}\right)$

Solution:

$\cos ^{-1}\left(\cos 680^{\circ}\right)=\cos ^{-1}\left[\cos \left(720^{\circ}-680^{\circ}\right)\right]$

$=\cos ^{-1}\left(\cos 40^{\circ}\right)$

$=40^{\circ}$

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