已知sin（pai—x）+cos（pai+x）=1/5（0

网友回答

∵sin(π-x)+cos(π+x)=1/5
==>sinx-cosx=1/5.(1)
==>(sinx-cosx)²=1/25
==>2sinxcosx=24/25
∴(sinx+cosx)²=sin²x+2sinxcosx+cos²x
=1+2sinxcosx
=1+24/25
=49/25
∴sinx+cosx=±7/5.(2)
∵0======以下答案可供参考======
供参考答案1:
原式=sin(x)-cos(x)=4/5-3/5=1/5;
=> tan(x)=sin(x)/cos(x)=4/3;