Let ${W\_t}$ be 1 dimension Brownian motion and
$X\_t:=\exp(t/2)\cos W\_t$ $t\in[0,T]$.

Show that $X\_t$ is martingale.

I understood $df(t,W\_t)=-\exp(t/2)\sin xdW\_t$
, but I don't know why it become $X\_t=1-\int\_0^t \sin X\_sdW\_s$.

$f(0,X\_0)=e^0 \sin X\_0=1$? $X\_0=?$

Please tell me.