Question

The range of the function [ sin x + cos x ] , where [.] denotes the greatest integer function​

Answer 1

Answer:

Range of |sinx| is [0,1] and |cosx| is [0,1] for all x belongs to R. So the range of f(x) is also [0,1] as sin0 =! cos0. So [|sinx| + |cosx|] = 1 as per the definition of greatest integer function.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

$Let \: f(x) =[ \sin(x) + \cos(x)]$

We know that,

$- \sqrt{2} \leqslant \sin(x) + \cos(x) \leqslant \sqrt{2}$

$\implies [ - \sqrt{2} ] \leqslant [ \sin(x) + \cos(x) ] \leqslant [ \sqrt{2} ]$

$\implies \: - 2 \leqslant f(x) \leqslant 1$

Hence, range of given function $\in [-2,1]$