Which of the following statements are correct?
(A) $\sin ^{-1}(-x)=-\sin ^{-1} x, x \in[-1,1]$
(B) $\tan ^{-1}(-x)=-\tan ^{-1} x,-1<x<1$
(C) $\cos ^{-1}(-x)=\pi-\cos ^{-1} x,-1 \leq x \leq+1$
(D) $\sec ^{-1}(-x)=\pi-\sec ^{-1} x,|x|>1$
(E) $\cot ^{-1}(-x)=\pi-\cot ^{-1} x, x \in R$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (E) Only
A. True
B. False, $\tan^{-1}(-x)=-\tan^{-1}x$ for $x∈R$
C. True
D. False, $\sec^{-1}(-x)=\pi - \sec^{-1}x$ for $|x|≥1$
E. True