1.已知sinα+cosα=(√2)/2,求sin^3α+cos^3α的值.(详解,注:√2表示根号2,sin^3α表示sinα的三次方)2.{cosα/(1+sinα)}-{sinα/(1+cosα)}={2(cosα-sinα)/(1+sinα+cosα)}(详解)3.已知sinα是方程5x^2-7x-6=0的根.求{cos(2
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 17:33:06
![1.已知sinα+cosα=(√2)/2,求sin^3α+cos^3α的值.(详解,注:√2表示根号2,sin^3α表示sinα的三次方)2.{cosα/(1+sinα)}-{sinα/(1+cosα)}={2(cosα-sinα)/(1+sinα+cosα)}(详解)3.已知sinα是方程5x^2-7x-6=0的根.求{cos(2](/uploads/image/z/5383133-53-3.jpg?t=1.%E5%B7%B2%E7%9F%A5sin%CE%B1%2Bcos%CE%B1%3D%28%E2%88%9A2%29%2F2%2C%E6%B1%82sin%5E3%CE%B1%2Bcos%5E3%CE%B1%E7%9A%84%E5%80%BC.%EF%BC%88%E8%AF%A6%E8%A7%A3%2C%E6%B3%A8%3A%E2%88%9A2%E8%A1%A8%E7%A4%BA%E6%A0%B9%E5%8F%B72%2Csin%5E3%CE%B1%E8%A1%A8%E7%A4%BAsin%CE%B1%E7%9A%84%E4%B8%89%E6%AC%A1%E6%96%B9%EF%BC%892.%7Bcos%CE%B1%2F%281%2Bsin%CE%B1%29%7D-%7Bsin%CE%B1%2F%281%2Bcos%CE%B1%29%7D%3D%7B2%28cos%CE%B1-sin%CE%B1%29%2F%281%2Bsin%CE%B1%2Bcos%CE%B1%29%7D%EF%BC%88%E8%AF%A6%E8%A7%A3%EF%BC%893.%E5%B7%B2%E7%9F%A5sin%CE%B1%E6%98%AF%E6%96%B9%E7%A8%8B5x%5E2-7x-6%3D0%E7%9A%84%E6%A0%B9.%E6%B1%82%7Bcos%282)
1.已知sinα+cosα=(√2)/2,求sin^3α+cos^3α的值.(详解,注:√2表示根号2,sin^3α表示sinα的三次方)2.{cosα/(1+sinα)}-{sinα/(1+cosα)}={2(cosα-sinα)/(1+sinα+cosα)}(详解)3.已知sinα是方程5x^2-7x-6=0的根.求{cos(2
1.已知sinα+cosα=(√2)/2,求sin^3α+cos^3α的值.(详解,注:√2表示根号2,sin^3α表示sinα的三次方)
2.{cosα/(1+sinα)}-{sinα/(1+cosα)}={2(cosα-sinα)/(1+sinα+cosα)}(详解)
3.已知sinα是方程5x^2-7x-6=0的根.求{cos(2π+α)cos(π+α)tan^2(2π+α)}/{sin(π+α)sin(2π-α)cot(-α)}的值.(详解)
1.已知sinα+cosα=(√2)/2,求sin^3α+cos^3α的值.(详解,注:√2表示根号2,sin^3α表示sinα的三次方)2.{cosα/(1+sinα)}-{sinα/(1+cosα)}={2(cosα-sinα)/(1+sinα+cosα)}(详解)3.已知sinα是方程5x^2-7x-6=0的根.求{cos(2
1.sin^3α+cos^3α=(sinα+cosα)(sin^2α+cos^2α-sinαcosα).(1)
因为sinα+cosα=(√2)/2
所以1+2sinαcosα=1/2
所以sinαcosα= -(1/4)代入(1)中=【(√2)/2)】(1+1/4)=(5√2)/8
2.因为,(1+sinx+cosx)^=1+sin^x+cos^x+2sinx+2cosx+2sinxcosx
=2+2sinx+2cosx+2sinxcosx=2(1+sinx)(1+cosx)
所以,2/(1+sinx+cosx)=(1+sinx+cosx)/[(1+sinx)(1+cosx)]
则,左式=2(cosα-sinα)/(1+sinα+cosα)
=(cosα-sinα))(1+sinx+cosx)/[(1+sinx)(1+cosx)]
=[cosα-sinα+cos^x-sin^x]/[(1+sinx)(1+cosx)]
=[cosx(1+cosx)-sinx(1+sinx)]/[(1+sinx)(1+cosx)]
=cosα/(1+sinα)-sinα/(1+cosα)=右式
故,得证
3.由5x平方-7x-6=0得(5x+3)(x-2)=0
所以x=-0.6或2
因为sinα大于等于-1小于等于1
所以X=-0.6
所以sinα=-0.6
[sin(-α-3π/2)sin(3π/2-α)tg平方α)]/[cos(π/2-α)cos(π/2+α)ctg(π-α)]
=[-cos平方αtg平方α]/[sin平方αctgα]
=sin平方α/[sinαcosα]
=tgα
=0.75或-0.75