Find the range of $f(x) = |\sin x| + |\cos x|, x ∈ R$.

$1 ≥f(x)≥\sqrt{2}$ $\sqrt{2}≤f(x)≤1$ $1 ≤f(x)≤\sqrt{2}$ None of these

$1 ≤f(x)≤\sqrt{2}$

$f(x) = |\sin x| + |\cos x|\,∀\, x ∈ R$ Clearly, f(x) > 0. Also, $f^2(x) = \sin^2 x + \cos^2 x + |2 \sin x \cos x| = 1 + |\sin 2x|$ Now, $0 ≤ |\sin zx|≤1$ $∴1 ≤ 1+|\sin zx|≤2$ $∴1 ≤ f^2(x)≤2$ or $1 ≤f(x)≤\sqrt{2}$