Which of the following statements are correct ?

(A) $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\left(\frac{x+y}{1-xy }\right), xy < 1 $

(B) $\tan^{-1}x+\tan^{-1}y = \pi + \tan^{-1}\left(\frac{x+y}{1-xy }\right), xy > 1 $

(C) $\sin^{-1}x+\cos^{-1}x=\frac{\pi }{2} , x \in (-1, 1)$

(D) $\tan^{-1}x+\cot^{-1}x=\frac{\pi }{2} , x \in R$

(E) $\cos^{-1}(-x) =-\cos^{-1}x,  x \in [-1, 1]$

Choose the correct answer from the options given below :

(A), (B), (D) Only