cos(a-35°)cos(a+25°）+sin(a-35°）sin(65°-a)=?

题目

cos(a-35°)cos(a+25°）+sin(a-35°）sin(65°-a)=?
没写错，我们考卷上就是这样的！

答案

写错了,sin(65-a)是cos
原式=cos(a-35)cos(a+25)+sin(a-35)sin(90-65+a)
=cos(a-35)cos(a+25)+sin(a-35)sin(a+25)
=cos[(a-35)-(a+25)]
=cos(-60)
=1/2