已知x、y都是锐角,sinx=4/5,cos(X十y)=5/13,求siny的值?
问题描述：
已知x、y都是锐角,sinx=4/5,cos(X十y)=5/13,求siny的值?
答
∵ 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