1.f(x)=[cos(3x/4)+cos(x/4+π/3)]^2+[sin(3x/4)-sin(x/4+π/3)]^2
=cos^2(3x/4)+sin^2(3x/4)+cos^2(x/4+π/3)+sin^2(x/4+π/3)
+2cos(3x/4)cos(x/4+π/3)-2sin(3x/4)sin(x/4+π/3)
=1+1+2cos(3x/4+x/4+π/3)=2cos(x+π/3)+2
单增区间(2kπ-π/3,2kπ+2π/3),单减区间(2kπ+2π/3,2kπ+5π/3),极值点2kπ-π/3,2kπ+2π/3,k∈Z
2.[-π/6,5π/6]包含一个极小值点2π/3,两个端点中f(-π/6)较大.所以最大值是f(-π/6)=根3+2,
最小值是f(2π/3)=0