设函数f(x)=sin(2X+π/4)+cos(2X+π/4)的化简

问题描述:

设函数f(x)=sin(2X+π/4)+cos(2X+π/4)的化简

解法一:f(x)=sin(2X+π/4)+cos(2X+π/4)=√2[√2/2sin(2X+π/4)+√2/2cos(2X+π/4)]=√2sin(2x+π/4+π/4)=√2sin(2x+π/2)=√2cos2x.解法二:f(x)=sin(2X+π/4)+cos(2X+π/4)=√2/2sin2x+√2/2cos2x+√2/2cos2x-√...