51问答网 > 数学题：已知COS(π⼀4-a)=3⼀5 sin（5π⼀4+b）=-12⼀13,a∈（π⼀4，3π⼀4），b∈(0,π⼀4)，求sin(a+b)

数学题：已知COS(π⼀4-a)=3⼀5 sin（5π⼀4+b）=-12⼀13,a∈（π⼀4，3π⼀4），b∈(0,π⼀4)，求sin(a+b)

额 好难的感觉 解答详细点哈
2025-04-06 21:57:51
推荐回答（1个）
回答1：

因为a∈（π/4，3π/4），b∈(0,π/4)，所以π/4-π/2<π/4-a<0,5π/4<5π/4+b<3π/2

cos(π/4-a)=3/5,sin（5π/4+b）=-12/13
则sin(π/4-a)=-4/5,cos(5π/4+b)=-5/13

sin(a+b)=-sin(π+a+b)=-sin[-(π/4-a)+(5π/4+b)]
=sin(π/4-a)*cos(5π/4+b)-cos(π/4-a)*sin(5π/4+b)
=-4/5*（-5/13）-3/5*（-12/13）
=56//65

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