数学三角恒等变换cos(x)+cos(y)=1/2,sin(x)+sin(y)=1/4,cos(x-y)=?

Question

数学三角恒等变换
cos(x)+cos(y)=1/2,sin(x)+sin(y)=1/4,cos(x-y)=?

Answer 1

[cos(x)+cos(y)]^2=1+2cos(x)cos(y)=1/4
[sin(x)+sin(y)]^2=1+2sin(x)sin(y)=1/16
两式加：2+4cos(x)cos(y)+2sin(x)sin(y)＝2+4cos(x-y)=5/16
4cos(x-y)=5/16-2＝-27/16
cos(x-y)=-27/64