Question

数学题：已知COS(π/4-a)=3/5 sin（5π/4 b）=-12/13,a∈（π/4，3π/4），b∈(-10,π/4)，求sin(a b)

Answer 1

a∈(π/4,3π/4)
π/4-a∈(-π,0)
sin(π/4-a)<0
sin²(π/4-a)+²cos²(π/4-a)=1
所以sin(π/4-a)=-4/5

sin(5π/4+b)
=sin(π+π/4+b)
=-sin(π/4+b)=-12/13
sin(π/4+b)=12/13
b∈(0,π/4)
π/4+b∈(π/4,π/2)
cos(π/4+b)>0
sin²(π/4+b)+cos²(π/4+b)=1
cos(π/4+b)=5/13

sin(a+b)=sin[(π/4+b)-(π/4-a)]
=sin(π/4+b)cos(π/4-a)-cos(π/4+b)sin(π/4-a)
=16/65