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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions3 Marks
Question
Write the difference between maximum and minimum values of $\sin^{-1}\text{x}$ for $\text{x}\in[-1,1].$
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Answer

We have to find the difference between maximum and minimum values of

$\sin^{-1}\text{x}$ for $\text{x}\in[-1,1]$

We know that,

$\sin^{-1}\text{x}=$ An angle in $\Big[-\frac{\pi}{2},\frac{\pi}{2}\Big]$ whose sin is x.

So, minimum value of $\sin^{-1}\text{x}=-\frac{\pi}{2}$

maximum value of $\sin^{-1}\text{x}=\frac{\pi}{2}$

Difference between maximum and minimum values of

$\sin^{-1}\text{x}=\frac{\pi}{2}-\Big(-\frac{\pi}{2}\Big)$

$=\frac{\pi}{2}+\frac{\pi}{2}$

$=\pi$

The required difference $=\pi.$

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