f(x)=1/2sin2xsinψ+COS²xcosψ-1/2sin(π/2+ψ),(0扫码下载作业帮拍照答疑一拍即得
问题描述：
f(x)=1/2sin2xsinψ+COS²xcosψ-1/2sin(π/2+ψ),(0
扫码下载作业帮
拍照答疑一拍即得
答
cos2x=2cos²x-1, ∴cos²x=(1+cos2x)/2
sin(π/2+￡)=cos￡
∴f(x)=(1/2)sin2xsin￡+(1+cos2x)/2×cos￡-(1/2)cos￡
=(1/2)sin2xsin￡+(1/2)cos2xcos￡+(1/2)cos￡-(1/2)cos￡
=(1/2)(cos2xcos￡+sin2xsin￡)=(1/2)cos(2x-￡)
x=π/6时,f(x)取得最大值, ∴cos(π/3-￡)=1
0解得 ￡=π/3
答
f(π/6)=√3/4sinψ+3/4cosψ-1/2cosψ
=√3/4sinψ+1/4cosψ
=1/2(√3/2sinψ+1/2cosψ)
=1/2sin(ψ+π/6)
=1/2
sin(ψ+π/6)=1
ψ+π/6=2kπ+π/2
ψ=2kπ+π/3,k∈Z