题目

已知sin(x-3/4π)cos(X-π/4)=-1/4,求cos4x的值.要过程

提问时间：2021-03-19

答案

sin(x-3/4π)=sin(x+π/4-π)=-sin(x+π/4)
也就是sin(x+π/4)cos(X-π/4)=1/4
sin(x+π/4)cos(X-π/4)=sin(x+π/4+x-π/4)+sin(x+π/4-x+π/4)=sin2xsinπ/2=sin2x=1/4
cos4x=1-2sin^2 2x=1-1/16=15/16