证明[2-2sin(α+3π/4)cos(α+π/4)]/(cos^4α-sin^4α)=(1+tanα)/(1-tan
来源:学生作业帮 编辑:灵鹊做题网作业帮 分类:数学作业 时间:2024/06/17 16:57:14
证明[2-2sin(α+3π/4)cos(α+π/4)]/(cos^4α-sin^4α)=(1+tanα)/(1-tanα)
证明:sin(α+3π/4)*cos(α+π/4)=sin[π/2+(α+π/4)]*cos(α+π/4)=cos(α+π/4)*cos(α+π/4)=cos��(α+π/4)=[√2/2*(cosα-sinα)]��=1/2(cosα-sinα)��;
2-2sin(α+3π/4)*cos(α+π/4)=2-(cosα-sinα)��=2-(cos��α+sin��α-2cosαsinα)=1+2cosαsinα=cos��α+sin��α+2cosαsinα=(cosα+sinα)��;
cos^4α-sin^4α=(cos��α)��-(sin��α)��=(cos��α-sin��α)(cos��α+sin��α)=(cosα-sinα)(cosα+sinα);
[2-2sin(α+3π/4)*cos(α+π/4)]/(cos^4α-sin^4α)=(cosα+sinα)��/(cosα-sinα)(cosα+sinα)=(cosα+sinα)/(cosα-sinα)=(1+tanα)/(1-tanα)
2-2sin(α+3π/4)*cos(α+π/4)=2-(cosα-sinα)��=2-(cos��α+sin��α-2cosαsinα)=1+2cosαsinα=cos��α+sin��α+2cosαsinα=(cosα+sinα)��;
cos^4α-sin^4α=(cos��α)��-(sin��α)��=(cos��α-sin��α)(cos��α+sin��α)=(cosα-sinα)(cosα+sinα);
[2-2sin(α+3π/4)*cos(α+π/4)]/(cos^4α-sin^4α)=(cosα+sinα)��/(cosα-sinα)(cosα+sinα)=(cosα+sinα)/(cosα-sinα)=(1+tanα)/(1-tanα)
证明[2-2sin(α+3π/4)cos(α+π/4)]/(cos^4α-sin^4α)=(1+tanα)/(1-tan
试证明:1+2sinαcosα/cos平方α-sin平方α=tan(π/4-α)
证明(2-2sin(α+3/4π)cos(α+π/4))/cos^4α-sin^4α=1=tanα/1-tana
求证:(1-sinα+cosα)/(1+sinα+cosα)=tan(π/4-α/2)
求证:1-2sinαcosα/cos²α-sin²α=tan(π/4-α)
求证(1-2sinαcosα)/(cos²α-sin²α)=tan(π/4-α)
一道高中三角函数题tanα/tanα-1=2,求下列各式的值.sinα-3cosα/sinα+cosα4sin²
证明tanα/2=1-cosɑ/sinɑ
已知tanα/2=2,求(1)tan(α-4/π)的值,(2)(3sinα+cosα)/(3cosα-sinα)
已知tan(α+π/4)=2,则(2sinα+cosα)/(3cosα-2sinα)
已知tan(α+π/4)=2,求2cosα-sinα/cosα+3sinα
已知tan(α+π/4)=3,求cosα+2sinα/cosα-sinα的值