Question

Range of f(x) = [|sinx| + |cosx|], where [.] denotes the greatest integer function, is

• A. {0}
• B. {0, 1}
• C. [1]
• D. None of these

Answer 1

Answer: (C)

$1$

Answer 2

y = |sinx| + |cosx|

⇒ y² = 1 + |sin2x|

⇒ 1 ≤ y² ≤ 2 ⇒ y ∈ [1, $\sqrt { 2 }$] ⇒ f(x) = 1 ∀ x ∈ R