Sin x-sin y=2/3 cos x-cos y=1/2 求cos(x-y)

题目

Sin x-sin y=2/3 cos x-cos y=1/2 求cos(x-y)

答案

Sin x-sin y=2/3
cos x-cos y=1/2
分别平方得
(Sin x-sin y)^2=(2/3)^2
(cos x-cos y)^2=(1/2)^2
展开相加得
-2cos(x-y)+2=4/9+1/4
-2cos(x-y)=1/2
cos(x-y)=-1/4