已知cosa-cosb=(根号5)/5,sina-sinb=(根号15)/5.(1)求cos(a-b)的值;(2)若0小于a小于pi/2,-pi/2小于b...

题目

已知cosa-cosb=(根号5)/5,sina-sinb=(根号15)/5.(1)求cos(a-b)的值;(2)若0小于a小于pi/2,-pi/2小于b...
已知cosa-cosb=(根号5)/5,sina-sinb=(根号15)/5.(1)求cos(a-b)的值;(2)若0小于a小于pi/2,-pi/2小于b小于0,且sinb=-5/13,求sina的值

答案

1.(cosa-cosb)^2+(sina-sinb)^2=(cosa)^2+(cosb)^2-2cosacosb+(sina)^2+(sinb)^2-2sinasinb
=2-2cos(a-b)=(√5/5)^2+(√15/5)^2=4/5
cos(a-b)=3/5
2.sina=sin(b+(a-b))=sinbcos(a-b)+cosbsin(a-b)