Question

已知cos（x+y）=5/13，cosy=4/5，xy都为锐角，求sinx的值。

Answer 1

X,Y都为锐角，sinX=5／13,cos(X+Y)=-4／5
所以cosx=12/13，sin(x+y)=3/5
cos(X+y)=cosxcosy-sinxsiny=12/13cosy-5/13siny=-4／5①
sin(x+y)=sinxcosy+cosxsiny=5/13cosy+12/13siny=3/5②
②×12-①×5，得144/13siny+25/13siny=36/5+20/5
则13siny=56/5
所以siny=56/65

Answer 2

由条件可得
siny=3/5 sin(x+y)=12/13
sinx=sin{(x+y)-y}
=sin(x+y)cosy-cos(x+y)siny
=(12/13) *(4/5)-(5/13)(3/5)
=33/65

Answer 3

sin(x y)=12/13.......x y比180°小
siny=3/5
cosx=cos[(x y)-y]=cos(x y)cosy sin(x y)siny=56/65
sinx=根号下1-cosx^2
关键是前面一步。。加油