设sinα+sinβ=1/3,则sinα-cos方β的最大值是

sinα+sinβ=1/3
sinβ=(1/3-sinα)
sinα-cos方β
=sinα-1+(sinβ)^2
=sinα-1+(1/3-sinα)^2
=(sinα)^2+(sinα)/3-8/9
=(sinα+1/6)^2-11/12
当sinα=1时,上式取最大值=4/9
B 4/9