f(x)=cos(2x-兀/3）+2sin(x-兀/4)sin(x+兀/4)怎么化简

题目

f(x)=cos(2x-兀/3）+2sin(x-兀/4)sin(x+兀/4)怎么化简

答案

积化和差f(x)=cos(2x-π/3）+2sin(x-π/4)sin(x+π/4)=cos(2x-π/3）+2×(-1/2){cos[(x-π/4)+(x+π/4)]-cos[(x-π/4)-(x+π/4)]}=cos(2x-π/3）-[cos2x-cos(-π/2)]=cos(2x-π/3）- cos2x=cos2xcos(π/3)+sin2xsin(...