已知0<β<π/4,π/4<α<3π/4,cos(π/4-α)=3/5,sin(3π/4+β)=5/13,求sin(α+β
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已知0<β<π/4,π/4<α<3π/4,cos(π/4-α)=3/5,sin(3π/4+β)=5/13,求sin(α+β
已知0<β<π/4,π/4<α<3π/4,cos(π/4-α)=3/5,sin(3π/4+β)=5/13,求sin(α+β
已知0<β<π/4,π/4<α<3π/4,cos(π/4-α)=3/5,sin(3π/4+β)=5/13,求sin(α+β
因为π/4<α+β<π,所以sin(α+β)>0,
因为
-π/2<π/4-α<0,
cos(π/4-α)=3/5,
所以sin(π/4-α)= -4/5;
因为
3π/4<β+3π/4<π
sin(3π/4+β)=5/13
所以cos(3π/4+β)= -12/13
sin(3π/4+β-(π/4 -α))=sin(α+β+π/2)= - cos(α+β)=(5/13)*(3/5)-(-12/13)*(-4/5)=-33/65
sin(α+β)=√(1-(33/65)∧2)=(√3116)/65
利用整体来求
即α+β=π/2-[(3π/4+β)-(π/4-α)]
已知π<α+β
已知π<a
已知sin=-4/5,π<α
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