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If the function $f (x) = \frac{ksinx + 2 cosx}{sinx + cosx}$ is strictly increasing for all values of x, the

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$k < 1$

$k > 1$

$k < 2$

$k > 2$

answer is D.

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Detailed Solution

$\begin{array}{l} f' (x) = \frac{Kcos 2 x + Ksin 2 x - 2 \cos^{2} x - 2 \sin^{2} x}{(sinx + cosx) 2} > 0 \\ = K - 2 > 0 \end{array}$

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