若x,y均为锐角,且sinx=根号10/10,siny=根号5/5,求证x+y=π/4

问题描述:

若x,y均为锐角,且sinx=根号10/10,siny=根号5/5,求证x+y=π/4

cosx=3√10/10
cosy=2√5/5
cos(x+y)=3√10/10×2√5/5-√10/10×√5/5=√2/2
x,y均为锐角
0°<x+y<180°
∴x+y=π/4