How you prove that sin(90+30)=cos30?

You need the identity
##sin(a+b)=sin(a)cos(b)+cos(a)sin(b)##
Just plugging in the numbers
##sin(90+30)=sin(90)cos(30)+cos(90)sin(30)=cos(30)##
Since ##sin(90)=1## and ##cos(90)=0##