3. The equation $2^{|2 x-2|}-a \cos (1-x)=0$ has only one real solution with respect to $x$, then
A. $a=-1$
B. $a=1$
C. $a=2$
D. The value of $a$ is not unique
The graph of the function $f(x)=2^{|2 x-2|}-a \cos (1-x)$ is symmetric about the line $x=1$, so $f(1)=0$ $\Rightarrow 1-a=0 \Rightarrow a=1$, hence the answer is $B$.

