已知sin(π-α)+sin(5π/2+α)=根号2/3(π/2

sin(π-α)+sin(5π/2+α)=√2/3
sinα+sin(π/2+α)=√2/3
sinα-cosα=√2/3为什么是这样算的？答案是4/3。如果你题目没有抄错的话答案错了使用的是诱导公式sin(π-α)=sinαsin(5π/2+α)=sin(π/2+α)=-cosα于是sin(π-α)+sin(5π/2+α)=√2/3sinα+sin(π/2+α)=√2/3sinα-cosα=√2/3也就是要求的值了谢谢。我上面错了,答案是正确的sin(5π/2+α)=sin(π/2+α)=cosα才对sin(π-α)=sinαsin(5π/2+α)=sin(π/2+α)=cosα于是sin(π-α)+sin(5π/2+α)=√2/3sinα+sin(π/2+α)=√2/3sinα+cosα=√2/3(sinα+cosα)²=(√2/3)²sin²α+cos²α+2sinαcosα=2/91+2sinαcosα=2/92sinαcosα=-7/9于是(sinα-cosα)²=sin²α+cos²α-2sinαcosα=1-（-7/9）=16/9∵π/20cosα0∴sinα-cosα=√(16/9)=4/3