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If the function $f (x) = \frac{k \sin x + 2 \cos x}{\sin x + \cos x}$ is strictly increasing for all values of $x$ , then

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$k < 1$

$k > 1$

$k < 2$

$k > 2$

answer is D.

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Detailed Solution

$f (x) = \frac{ksin x + 2 \cos x}{\sin x + \cos x} \Rightarrow f (x) = \frac{k \tan x + 2}{\tan x + 1} f^{'} (x) = \frac{k - 2}{{(\tan x + 1)}^{2}} s e c^{2} x$

$f (x) is increasing$ $f^{'} (x) > 0$
$k - 2 > 0 \Rightarrow k > 2$

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