(1)f(x)=cos^2X+2asinX-1
=-sinX^2+2asinX
=-(sinX-a)^2+a^2
0≤x≤2π ,-1≤sinX≤1
a＞1,sinX=1时,f(x)最大值为a^2
选D
（2）证明：sin(x+y)=1
x+y=π/2+2kπ
2x+y=π/2+2kπ+x
tan(2x+y)+tan y
= tan(π/2+2kπ+x)+tan(π/2+2kπ-x)
=tan(π/2+x)+tan(π/2-x)
=-cotx+cotx
=0