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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
Question
Find the principal value of cosec–1 (2)
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Answer

Let cosec-1 2 = x
Therefore, cosec x = 2 =cosec $\left(\frac{\pi}{6}\right)$
and cosec $\left(\frac{\pi}{6}\right)$ = 2
We know that the principle value range of cosec-1 is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$
Therefore, principle value of cosec-1(2) is $\frac{\pi}{6}$

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