已知0<β<45°,45°<α<135°,cos(45°-α)=3/5,sin(135°+β)=5/13,求sin(α+β)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/19 16:41:02
已知0<β<45°,45°<α<135°,cos(45°-α)=3/5,sin(135°+β)=5/13,求sin(α+β)已知0<β<45°,45°<α<135°,cos(45°-α)=3/5,si

已知0<β<45°,45°<α<135°,cos(45°-α)=3/5,sin(135°+β)=5/13,求sin(α+β)
已知0<β<45°,45°<α<135°,cos(45°-α)=3/5,sin(135°+β)=5/13,求sin(α+β)

已知0<β<45°,45°<α<135°,cos(45°-α)=3/5,sin(135°+β)=5/13,求sin(α+β)
由于0

由于0得sin(45°-A)=-4/5,cos(135°+B)=-12/13
45°所以sin(A+B)>0
sin(A+B)=-cos(90°+A+B)
=-cos[(135°+B)-(45°-A)]
=56/65