题目内容：

已知a(√1-b²)+b(√1-a²)=1,求证：a²+b²＝1.（让我看明白并态度认真的,

优质解答

|a|,|b|
sin(x)cos(y)+sin(y)cos(x)=1
sin(x+y)=1
x+y=π/2
sin(x)=cos(y)
a^2+b^2=sin(x)^2+sin(y)^2=cos(y)^2+sin(y)^2=1