1.sin(π/4+x)*sin(π/4+x)-cos(π/4+x)*cos(π/4+x)2.cosα*cos(α+β)-sin(α+β)*sinα3.cos(α-β)*cos(β-ν)-sin(α-β)*cos(β-ν)

来源:学生作业学帮网 编辑:学帮网 时间:2024/05/13 23:37:21

1.sin(π/4+x)*sin(π/4+x)-cos(π/4+x)*cos(π/4+x)
2.cosα*cos(α+β)-sin(α+β)*sinα
3.cos(α-β)*cos(β-ν)-sin(α-β)*cos(β-ν)

1. sin(π/4+x)*sin(π/4+x)-cos(π/4+x)*cos(π/4+x)
=-{[cos(π/4+x)]^2-[sin(π/4+x)]^2}
=-cos[2*(π/4+x)]
=-cos(π/2+2x)
=sin(2x)
2.cosα*cos(α+β)-sin(α+β)*sinα
=cos[α+(α+β)]
=cos(2α+β)
3.cos(α-β)*cos(β-ν)-sin(α-β)*cos(β-ν)
=sin[(α-β)-(β-ν)]
=sin(α+ν-2β)