已知函数f(x)=(sinx+cosx)^2+cos2x的最小值是

问题描述:

已知函数f(x)=(sinx+cosx)^2+cos2x的最小值是

f(x)=(sinx+cosx)^2+cos2x =sin^2x+2sinxcosx+cos^2x+cos2x=1+sin2x+cos2x=√2(sin2x*√2/2+cos2x*√2/2)+1 =√2(sin2xcosπ/4+cos2xsinπ/4)+1 =√2sin(2x+π/4)+1所以当sin(2x+π/4)=-1时有...