解 f(2012)=asin(2012π+α)+bcos(2012π+β)+1
=asinα+bcosβ+1
所以asinα+bcosβ=2011
f(2013)=asin(2013π+α)+bcos(2013π+β)+1
=asin(π+α)+bcos(π+β)+1
=-（asinα+bcosβ ）+1
=-2011+1
=-2010