Consider the following in respect of inverse circular functions :
I. $\sin^{-1}(-x)=-\sin^{-1}x$
II. $\cos^{-1}(-x)=\cos^{-1}x$
III. $\tan^{-1}(-x)=\pi-\tan^{-1}x$
IV. $\cot^{-1}(-x)=\pi-\cot^{-1}x$
How many of the above are correct ?

Statement I: $\sin^{-1}(-x) = -\sin^{-1}x$ is a standard property of inverse trigonometric functions and is correct.

Statement II: The correct property is $\cos^{-1}(-x) = \pi - \cos^{-1}x$. Hence, this statement is incorrect.

Statement III: The correct property is $\tan^{-1}(-x) = -\tan^{-1}x$. Hence, this statement is incorrect.

Statement IV: $\cot^{-1}(-x) = \pi - \cot^{-1}x$ is a standard property and is correct.

Exactly two of the given statements are correct.