f(x)=(cos²x+sin²x)(cos²x-sin²x)-sin2x
=cos2x-sin2x
=-√2sin(2x-π/4)
所以sin(2x-π/4)=1时最小
2x-π/4=2kπ+π/2
所以最小值=-√2
x∈{x|x=kπ+3π/4}