Question

已知a√1-b² +b√1-a² =1,求a²+b²的值

Answer 1

令a=sin(m),b=sin(n).带入原式得sin(m+n)=1,进而m+n=90°,即b=sin(n)=sin(90°-m)=cos(m)将a=sin(m),b=cos(m)代入a²+b²,得a²+b²=sin²(m)+cos²(m)=1