Question

a大于45度，小于135度，b大于0小于45度cos（45+a）=-3/5，sin（135+b）=13分之5则sin（a+b）

Answer 1

45<a<135 =>90<45+a<180第2象限; cos(45+a)=-3/5 =>sin(45+a)=4/5 (正)
0<b<45 =>135<135+b<180第2象限 ; sin(135+b)=5/13 =>cos(135+b)=-12/13(负)
sin(45+a + 135+b)=sin(180+a+b)= -sin(a+b)
=sin(45+a)cos(135+b)+cos(45+a)sin(135+b)=(4/5)*(-12/13)+(-3/5)*(5/13)=(-48/65) +(-15/65)
=-63/65 => sin(a+b)=63/65...ans

Answer 2

由题意得，sin(45+a)=4/5,cos(135+b)=-12/13 (a大于45度，小于135度，b大于0小于45度.则a+45大于90度，小于180度，b+135大于135小于180度）
√2cosa/2-√2sina/2=-3/5 ①(将cos(45+a)=-3/5展开)
√2sina/2+√2cosa/2=4/5 ②（将sin(45+a)=4/5展开)
联立①②得
cosa=√2/10,sina=7√2/10

√2cosb/2-√2sinb/2=5/13 ③将sin(135+b)=5/13展开
-√2cosb/2-√2sinb/2=-12/13 ④将cos(135+b)=-12/13展开
联立③④得
cosb=17√2/26,sinb=7√2/26

sin(a+b)=sina.cosb+cosa.sinb=7√2/10x17√2/26+√2/10x7√2/26
=119/130