If the function $\frac{\cos \mathrm{x}+\mathrm{k} \sin \mathrm{x}}{2 \cos \mathrm{x}+3 \sin \mathrm{x}}$ is decreasing in its domain then $\mathrm{K}\in$

$$\begin{gathered} \text{⨍(x) =}\frac{\cos \text{ x+k sin x}}{2 \cos \mathrm{x}+3 \sin \mathrm{x}} \\ {\text{⨍}}^1\text{(x)=(2 cos x+3 sin x) (-sin x+k cos x)} \\ \frac{-(\cos \mathrm{x}+\mathrm{k} \sin \mathrm{x}) (-2\sin \mathrm{x}+3 \cos \mathrm{x})}{{(2 \cos \mathrm{x}+3 \sin \mathrm{x})}^2} \\ =-2 \sin \mathrm{x} \cos \mathrm{x}+2\mathrm{k} {\cos }^2\mathrm{x}-3 {\sin }^2\mathrm{x}+3\mathrm{k} \sin \mathrm{x} \cos \mathrm{x}+2 \sin \mathrm{x} \cos \mathrm{x} \\ \frac{-3 {\cos }^2\mathrm{x}+2\mathrm{k} {\sin }^2\mathrm{x}-3\mathrm{k} \sin \mathrm{x} \cos \mathrm{x}}{{(2 \cos \mathrm{x}+3 \sin \mathrm{x})}^2} \\ =\frac{2\mathrm{k}-3}{{(2 \cos \mathrm{x}+3 \sin \mathrm{x})}^2} \end{gathered}$$

$\text{⨍(x)}$ is decreasing

$$\begin{gathered} \Rightarrow {\text{⨍}}^1\text{(x)<0} \\ 2\mathrm{k}-3<0 \\ \mathrm{k}<\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \end{gathered}$$