If $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sinx}-\mathrm{cosx}-\mathrm{ax}+\mathrm{b}$ decreases for all $\mathrm{x}\in \mathrm{R}$ then

$$\begin{gathered} \begin{array}{l}Given f\left(x\right)=\sin x-\cos x-ax+b\\ diff w.r.to x on both sides\\ f\text{'}\left(x\right)=\cos x+\sin x-a\\ \sin ce f\left(x\right) is decrea\sin g function then \\ {\mathrm{f}}^1\left(\mathrm{x}\right)<0\\ \Rightarrow \cos \mathrm{x}+\sin \mathrm{x}<\mathrm{a} \\ \text{ dividing both sides by }\sqrt{2}\\ \Rightarrow \frac{1}{\sqrt{2}}\cos x+\frac{1}{\sqrt{2}}\sin x<\frac{a}{\sqrt{2}}\\ \Rightarrow \sin (x+\frac{\pi }{4})<\frac{a}{\sqrt{2}}\\ \therefore 1<\frac{a}{\sqrt{2}}\\ \Rightarrow a>\sqrt{2}\\ \end{array} \end{gathered}$$
$\mathrm{a}>\sqrt{2}$