Question

求cosa=4/5,cos(a+β)=3/5,且a,β均为锐角,求sin2β

Answer 1

cosa=4/5,sina=3/5 cos(a+β)=3/5,sin(a+β)=4/5或-4/5 cosβ=cos[(a+β)-a]=cos(a+β)cosa+sin(a+β)sina 当sin(a+β)=-4/5时 cosβ=(3/5)(4/5)-(4/5)(3/5)=0,β=90度,与β是锐角矛盾（舍弃） 当sin(a+β)=4/5时 cosβ=(3/5)(4/5)+(4/5)(3/5)=24/25 sinβ=7/25 sin2β=2sinβcosβ=2(7/25)(24/25)=336/625