Question 746558
You must have been taught about trigonometric identities for sum of angles, difference, double angle, and/or half angle.
One of those identities is
{{{sin (A+B)=sin(A)*cos(B)+cos(A)*sin(B)}}}
If you replace {{{A=25^o}}} and {{{B=35^o}}} you get
{{{sin (25^o+35^o)=sin(25^o)*cos(35^o)+cos(25^o)*sin(35^o)}}}
where the right hand side is the expression you have to evaluate.
Since {{{25^o+35^o=60^o}}} we can substitute to get
{{{sin(60^o)=ssin(25^o)*cos(35^o)+cos(25^o)*sin(35^o)}}} or
{{{sin(25^o)*cos(35^o)+cos(25^o)*sin(35^o)=sin(60^o)}}}
You should know that the exact value of {{{sin (60^o)}}} is {{{sqrt(3)/2}}}
so 
{{{highlight(sin(25^o)*cos(35^o)+cos(25^o)*sin(35^o)=sqrt(3)/2)}}}