Question

设函数f(x)=sin(2X+π/4)+cos(2X+π/4)的化简

Answer 1

解：
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-√2/2sin2x
=√2cos2x.

Answer 2

f(x)=sin(2X+π/4)+cos(2X+π/4)=sin2x*cosπ/4+cos2xsinπ/4+cos2xcosπ/4-sin2xsinπ/4=
根号2*sin2x/2+根号2*cos2x/2+根号2*cos2x/2-根号2*sin2x/2=根号2cos2x=
2根号2（cosx）^2-根号2