已知锐角a,β满足cosa=3/5,cos(a+β)=－5/13,则cosβ=

题目

已知锐角a,β满足cosa=3/5,cos(a+β)=－5/13,则cosβ=

答案

cosa=3/5,sina=4/5
cos(a+β)=－5/13,sin(a+β)=12/13
cosβ
=cos[(a+β)-a]
=cos(a+β)cosa+sin(a+β)sina
=－5/13*(3/5)+12/13*(4/5)
=33/65