Choose the correct answer.
A. $\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}, x \in[-1,1]$
B. $\cos ^{-1}(-x)=-\cos ^{-1} x, x \in[-1,1]$
C. $\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}, x \in(-1, 1)$ only
D. $\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}, x \in R$
E. $\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right), x y<1$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) - A, D and E only
A. True
B. false, $\cos^{-1}(-x)=\pi -\cos ^{-1} x, x \in[-1,1]$
C. false, $\sin^{-1} x+\cos^{-1} x=\frac{\pi}{2}$, for $x \in[-1, 1]$
D. true
E. true