Question

已知sinx-siny=-2/3,COSX-COSY=2/3,且X,Y为锐角，则SIN(X+Y)=?

Answer 1

sinx-siny+cosx-coy=0,所以sinx+cosx=siny+cosy,两边平方得1+2sinxcosx=1+2sinycosy,所以2sinxcosx=2sinycosy,即sin2x=sin2y,所以2x=2y或2x+2y=π,由sinx-siny=-2/3得2x+2y=π,所以x+y=π/2,所以sin(x+y)=sinπ/2=1

Answer 2

sinx-siny=-2/3 COSX-COSY=2/3 分别平方 有sinx²+siny²-2sinxsiny=4/9
COSX²+COSY²--2COSXCOSY=4/9二式相加
有COSX²+COSY²--2COSXCOSY+sinx²+siny²-2sinxsiny=COSX²+sinx²+COSY²+siny²—2(COSXCOSY+sinxsiny)=2—cosx-y=8/9 所以cosx-y=10/9 奥 不小心算成了cosx-y

Answer 3

2cos(x+y)/2*sin(x-y)/2=-2/3;-2sin(x+y)/2*sin(x-y)/2=2/3,
tan(x+y)/2=1,(x+y)/2=π/4, x+y=π/2,sin(x+y)=1