已知π/4＜a＜3π/4,0＜B

Question

已知π/4＜a＜3π/4,0＜B

Answer 1

已知：π/4＜a＜3π/4,0＜b＜π/4.cos(π/4+a)=-3/5,sin(3π/4+b)=5/13,则sin(a+b)的值
已知a,b定义域
sin(π/4+a)=4/5
cos(3π/4+b)=12/13
sin(a+b+π)=sin[(π/4+a)+(3π/4+b)]
=sin(π/4+a)cos(3π/4+b) + cos(π/4+a)sin(3π/4+b)
=4/5 x 12/13 + (-3/5) x 5/13
=35/65
所以
sin(a+b)=-sin(a+b+π)=- 35/65