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 ?

Question

Consider the following in respect of inverse circular functions : I. ^ -1 (-x)=- ^ -1 x II. ^ -1 (-x)= ^ -1 x III. ^ -1 (-x)=π- ^ -1 x IV. ^ -1 (-x)=π- ^ -1 x How many of the above are correct ?

Quantrex Academy · Accepted Answer

Correct answer: B. Two

Statement I: ^ -1 (-x) = - ^ -1 x is a standard property of inverse trigonometric functions and is correct. Statement II: The correct property is ^ -1 (-x) = π - ^ -1 x . Hence, this statement is incorrect. Statement III: The correct property is ^ -1 (-x) = - ^ -1 x . Hence, this statement is incorrect. Statement IV: ^ -1 (-x) = π - ^ -1 x is a standard property and is correct. Exactly two of the given statements are correct.

Consider the following in respect of inverse circular functions :...

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