0<β<π⼀4<α<3π⼀4,cos(π⼀4-α)=3⼀5,sin(3π⼀4+β)=5⼀13,求sin(α+β)

0&lt;β&lt;π/4&lt;α&lt;3π/4,cos(π/4-α)=3/5,sin(3π/4+β)=5/13,求sin(α+β)
2025-04-18 18:24:26
推荐回答(1个)
回答1:

0<β<π/4<α<3π/4,cos(π/4-α)=3/5,sin(3π/4+β)=5/13,
-π/2<π/4-α<0 3π/4<3π/4+β<π
cos(3π/4+β)=-12/13 sin((π/4-α)=-4/5
sin(α+β)=sin[(3π/4+β)-(π/4-α)-π/2]=-cos[(3π/4+β)-(π/4-α)]
=-cos(π/4-α)*cos(3π/4+β)*-sin(3π/4+β)sin(π/4-α)
=-3/5*(-12/13)-5/13*(-4/5)
=56/65