已知x,y∈R+,且x1-y2+y1-x2=1,则x2+y2=______.-数学

题目简介

已知x,y∈R+,且x1-y2+y1-x2=1,则x2+y2=______.-数学

题目详情

已知x,y∈R+,且
1-y2
+y 
1-x2
=1
,则x2+y2=______.
题型:填空题难度:中档来源:韶关三模

答案

令x=sinA,y=sinB,其中A,B∈[0,class="stub"π
2
]
∴cosA=
1-x2
  cosB=
1-y2

1-y2
+y 
1-x2
=1

∴sinAcosB+sinBcosA=1即sin(A+B)=1
∴A+B=class="stub"π
2
,A=class="stub"π
2
-B
sinA=sin(class="stub"π
2
-B)=cosB
∴x2+y2=sin2A+sin2B=sin2(class="stub"π
2
-B)+sin2B=cos2B+sin2B=1
故答案为:1.

更多内容推荐