A. $f(x)=|x|$ is continuous function on R (the set of real numbers)
B. $f(x)=[x]$ is continuous function on R.
C. $f(x)=\sin x$ is continuous function on R.
D. $f(x)=\tan x$ is continuous function on R.
E. $f(x)=\sin x+\cos x$ is continuous function on R.

Choose the correct answer from the options given below:

A, C, E only

The correct answer is Option (3) → A, C, E only

(A) True

(B) False, [x] is not continuous on integral values.

(C) True

(D) False, $\tan x$ is discontinuous for $x=(2n-1)\frac{π}{2}$

(E) True