△ABC中,a,b,c分别是角A,B,C的对边,且sin(B+π/4)-sin(B-π/4)=根号2/2,(1)求角B大小;_数学解答

△ABC中,a,b,c分别是角A,B,C的对边,且sin(B+π/4)-sin(B-π/4)=根号2/2,(1)求角B大小;

人气：366 ℃　时间：2019-11-04 17:15:34

解答

sin(B+π/4)-sin(B-π/4)=√2/2
sinBcos(π/4)+cosBsin(π/4)-(sinBcos(π/4)-cosBsin(π/4))=√2/2
2cosBsin(π/4)=√2/2
√2cosB＝√2/2
cosB＝1/2
B=60°