一道数学题函数y=log1/2(sin2x+cos2x)的递减区
y=log1/2(sin2x+cos2x)的递减区间为________.
y=log<1/2>(sin2x+cos2x)=log<1/2>[√2sin(2x+π/4)], 由sin(2x+π/4)]>0,得,2kπ<2x+π/4<2kπ+π, ∴ 定义域(kπ-π/8,kπ+3π/8)(k∈Z). 由2kπ+π/2<2x+π/4<2kπ+π,得kπ+π/8