三角形ABC为锐角三角形,a,b,c为A,B,C对边,且(sinA)^2=sin(π/3+B)sin(π/3-B)+(sinB)^2,求A
问题描述:
三角形ABC为锐角三角形,a,b,c为A,B,C对边,且(sinA)^2=sin(π/3+B)sin(π/3-B)+(sinB)^2,求A
答
∵(sinA)ˆ2=sin(π/3+B)sin(π/3-B)+sin(B)ˆ2∴ (sinA)ˆ2=(sinπ/3cosB+cosπ/3sinB)(sinπ/3cosB-cosπ/3sinB)+sin(B)ˆ2∴ (sinA)ˆ2=[(3ˆ1/2)/2cosB+1/2sinB][3ˆ1/2)/2cosB-1/...