一.设△ABC的角A.B.C的对边长为a.b.c,且3b^2+3c^2-3a^2=四倍根号二倍的bc.求①sinA的值②求2sin(A+π/4)sin(B+C+π/4)除以(1-cos2A)的值.
问题描述:
一.设△ABC的角A.B.C的对边长为a.b.c,且3b^2+3c^2-3a^2=四倍根号二倍的bc.求①sinA的值②求2sin(A+π/4)sin(B+C+π/4)除以(1-cos2A)的值.
二.在△ABC中,A.B.是锐角,角A.B.C所对的边为a.b.c,且cos2A=3/5,sinB=十分之根号十.求①A+B的值②若a-b=根号二减一,求a.b.c的值.
答
一,①cosA=(b^2+c^2-a^2)/2bc3b^2+3c^2-3a^2=(4根号2)bc(b^2+c^2-a^2)/2bc=(2根号2)/3cosA=(2根号2)/3sinA=1/3②2sin(A+π/4)sin(B+C+π/4)/(1-cos2A)=2sin(A+π/4)sin(π-A+π/4)/(2sin^2A)=sin(A+π/4)sin...