Mark the correct alternative in the following:

Formula:- (i) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on $(a, b)$ is that $f^{\prime}(x)>0$ for all $x \in(a, b)$

Given:-

$f(x)=\frac{\lambda \sin x+2 \cos x}{\sin x+\cos x}$

For increasing function $f^{\prime}(x)<0$

$\frac{\mathrm{d}(\mathrm{f}(\mathrm{x}))}{\mathrm{dx}}=\mathrm{f}^{\prime}(\mathrm{x})=\frac{\lambda-2}{(\sin \mathrm{x}+\cos \mathrm{x})^{2}}>0$

$\Rightarrow \lambda>2$