Evaluate the following: ^ -1 ( 25 6 )

Question

Evaluate the following:
$\sec^{-1}\Big(\sec\frac{25\pi}{6}\Big)$

✓

Answer

We have
$\sec^{-1}\Big(\sec\frac{25\pi}{6}\Big)=\sec^{-1}\Big[\sec\Big(4\pi+\frac{\pi}{6}\Big)\Big]$
$=\sec^{-1}\Big[\sec\Big(\frac{\pi}{6}\Big)\Big]$
$=\frac{\pi}{6}$

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