已知y1=sin(x),y2=sin(x+a),y3=sin(x+b)三者存在如下关系,(y1-y3)(y1-y3)+(y2-y3)(y2-y3)=1;求a和b的关系

Question

已知y1 = sin(x),y2 = sin(x+a),y3 = sin(x+b) 三者存在如下关系,(y1-y3)(y1-y3)+(y2-y3)(y2-y3) = 1;
求a和b的关系

Answer 1

[sin(x)-sin(x+b)]^2+[sin(x+a)-sin(x+b)]^2=1
sin^(x)+sin^(x+a)+2sin^(x+b)+2sin(x)sin(x+b)+2sin(x+a)sin(x+b)=1
sin^(x)+sin^(x+a)+cos(b)-cos(2x+b)+cos(a-b)-cos(2x+a+b)=cos(2x+2b)