Question

cos(π/4-α)=3/5,sin(5π/4+β)=-12/13,α∈(π/4,3π/4),β∈(0,π/4),求sin(α+β）的值

Answer 1

α∈(π/4,3π/4),β∈(0,π/4),( π/4-α ) ∈(-π/2,0 ） (5π/4+β)∈(5π/4,3π/2)所以有sin(π/4-α)=-√[1-(cos(π/4-α))^2]=-4/5 cox(5π/4+β)=-√[1-(sin(5π/4+β))^2]=-5/12sin(α+β）=-sin((5π/4+β)-(π/4-α))=-(sin(5π/4+β)cos(π/4-α)- cos(5π/4+β)sin(π/4-α))=173/195

Answer 2

sin (a ＋B)=-sin <(5 /4 ＋B)-(1/4 -a )>=sin(5/4＋B)cos(1/4-a) -cos(5/4＋B) sin(1/4-a) =16/65圆周率自己写