Question

已知x、y都是锐角,sinx=4/5,cos(X十y)=5/13,求siny的值?

Answer 1

∵ x、y 都是锐角,sinx=4/5 ,cos(x+y)=5/13

∴ cosx=3/5,sin(x+y)=12/13

∵ cos(x+y)=cosx*cosy-sinx*siny

sin(x+y)=sinx*cosy+cosx*siny

∴ 3/5cosy-4/5siny=5/13

4/5cosy+3/5siny=12/13

解得siny=16/65