There are four forces acting at a point $P$ produced by strings as shown in figure, which is at rest. The forces $F_1$ and $F_2$ are

Applying equilibrium conditions, $\underset{ }{\sum F_x=0}$

$\Rightarrow F_1+1\sin {45}^{\circ }-2\sin {45}^{\circ }$ or $F_1=2\sin {45}^{\circ }-1\sin {45}^{\circ }=\frac{2}{\sqrt{2}}-\frac{1}{\sqrt{2}}=\frac{2-1}{\sqrt{2}}=\frac{1}{\sqrt{2}}N$

and $\sum _{ }{F}_y=0\Rightarrow 1\cos {45}^{\circ }+2\cos {45}^{\circ }-F_2=0$

$F_2=\frac{2}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{2+1}{\sqrt{2}}=\frac{3}{\sqrt{2}}N$