Question

y=sin(ωx+φ)+cos(ωx+φ)的最小正周期是π,且f(-x)=f(x)则

Answer 1

（A）y＝f(x)在(0,π/2)单调递减（B）y＝f(x)在（π/4,3π/4）单调递减（C）y＝f(x)在（0,π/2）单调递增(D）y＝f(x)在（π/4,3π/4）单调递增

解析：∵函数f(x)=sin(wx 十φ) 十cos(wx十 φ)(|φ|0)的最小正周期为π,且f(-x)=f(x)

∴f(x)=sin(wx十 φ)十 cos(wx十 φ)=√2sin(wx 十φ 十π/4)

∴f(x)=2sin(2x十 φ 十π/4)

∵f(-x)=f(x)

∴φ π/4=π/2==>φ=π/4===>f(x)=√2cos(2x)

∴f(x)在(0,π/2)单调递减,A正确

选择A