Question

已知函数f(x)=cos⁴x-2sinxcosx-sin⁴x.

(1)求f(x)的最小正周期;

(2)若x∈［0, ］,求f(x)的最大值、最小值.

Answer 1

解析:f(x)=(cos²x+sin²x)(cos²x-sin²x)-sin2x

=cos2x-sin2x=2cos(2x+).

(1)T==π.

(2)0≤x≤,0≤2x≤π,≤2x+≤,-1≤cos(2x+)≤,∴-2≤2cos(2x+)≤1.

∴f(x)_max=1,f(x)_min=-2.

答案:(1)π;(2)f(x)_max=1,f(x)_min=-2.