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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions2 Marks
Question
Evaluate the following:
$\sec^{-1}\Big(\sec\frac{5\pi}{4}\Big)$
✓

Answer

We have
$\sec^{-1}\Big(\sec\frac{5\pi}{4}\Big)$
$=\sec^{-1}\Big(\sec\Big(\pi+\frac{\pi}{4}\Big)\Big)$
$=\sec^{-1}\Big(-\sec\Big(\frac{\pi}{4}\Big)\Big)$
$=\sec^{-1}\big(-\sqrt2\big)$
$=\frac{3\pi}{4}$

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