Question

当0<x<派/4时，函数f(x)=cos^2 x/cos xsin x-sin^2 x的最小值是

Answer 1

分子
分母
都除以cos^2x
f(x)=cos^2
x/cos
xsin
x-sin^2
x
=1/[tanx-(tanx)^2]
=1/[-(tanx-1/2)^2+1/4]
当tanx=1/2时
函数有最小值为4

Answer 2

f(x)
=
-cos2xcos5π/4+sin2xsin9π/4
=
-cos2xcos(π+π/4)+sin2xsin(2π+π/4)
=
cos2xcosπ/4+sin2xsinπ/4
=
sin(2x+π/4)
2x+π/4属于（2kπ-π/2，2kπ+π/2）时单调增；2x+π/4属于（2kπ+π/2，2kπ+3π/2）时单调减
单调增区间：（kπ-3π/8，kπ+π/8）
单调增区间：（kπ+π/8，kπ+5π/8）
最小正周期2π/2=π
最大值1
最小值-1