[tex]\sqrt2 -1\approx 0.4 \Rightarrow \sqrt2 -1 \in (0,1)[/tex]
[tex]|x|[/tex] is always non-negative, so the range of [tex](\sqrt2-1)^{|x|}[/tex] is [tex](0,1][/tex]
The range of [tex]\sin x[/tex] is [tex][-1,1][/tex] => the range of [tex]\sin^2x [/tex] is [tex][0,1][/tex] => the range of [tex]\sin^2x+1[/tex] is [tex][1,2][/tex]
The only common point of these two function is the one with y-coordinate = 1, so [tex]y=1[/tex]. Let's take one of these functions and find for which x, its value is equal to 1. I'll take the first one.
[tex](\sqrt2-1)^{|x|}=1\\
\Downarrow\\
|x|=0\\
x=0[/tex]
So, [tex]x=0[/tex] :)
