I am familiar with the importance of the following inverse circular/hyperbolic functions:(adsbygoogle = window.adsbygoogle || []).push({});

##\sin^{-1}##, ##\cos^{-1}##, ##\tan^{-1}##, ##\sinh^{-1}##, ##\cosh^{-1}##, ##\tanh^{-1}##.

However, I don't really get the point of ##\csc^{-1}##, ##\coth^{-1}##, and so on.

Given any equation of the form ##f(x) = a##, where ##f## is the reciprocal of any circular/hyperbolic function, we can always write the equation as ##\frac{1}{f(x)} = \frac{1}{a}## before solving it with the aid of the six aforementioned inverse functions.

For instance, ##\csc{x} = 2##, ##0 < x < 2\pi##.

##\csc{x} = 2##

##\sin{x} = \frac{1}{2}##

##x = \frac{\pi}{6}, \frac{5\pi}{6}##

Do we use them to avoid cluttered notation in calculus?

For example, for ##x \geq 1##:

$$\int \frac{1}{1 - x^2} dx = \coth^{-1}{x} + C = \frac{1}{2} \ln{\frac{x + 1}{x - 1}} + C$$

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# Inverse trigonometric functions

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