First we expand the expression $sinx+cosx$^2:

$si{n}^2(x)+2sinx\ast cosx+co{s}^2(x)$

Now we divide this expression by sin$2x$+1:

$si{n}^2(x)+2sinx\ast cosx+co{s}^2(x)$ / $sin(2x)+1$

We know that sin$2x$ = 2sinxcosx, so we can substitute this into our expression:

$si{n}^2(x)+2sinx\ast cosx+co{s}^2(x)$ / $2sinxcosx+1$

At this point, the expression can't be simplified any further.