Question

已知α，β均为锐角，tana=3/4,cos(α+β)=-5/13,求cosβ的值

sec是什么

Answer 1

a为锐角,tana=3/4
sec²a=1+tan²a=25/16
seca=5/4,cosa=4/5,sina=3/5
cos(a+β)=-5/13,易得sin(a+β)=12/13
cosβ=cos[(a+β)-a]
=cos(a+β)cosa+sin(a+β)sina
=-5/13*4/5+12/13*3/5
=-20/65+36/65
=16/65

seca=1/cosa