已知sin(2π-α)-cos(2π+α)=-√2/3(π/2

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/21 21:00:16
已知sin(2π-α)-cos(2π+α)=-√2/3(π/2已知sin(2π-α)-cos(2π+α)=-√2/3(π/2已知sin(2π-α)-cos(2π+α)=-√2/3(π/2sin(2π-

已知sin(2π-α)-cos(2π+α)=-√2/3(π/2
已知sin(2π-α)-cos(2π+α)=-√2/3(π/2

已知sin(2π-α)-cos(2π+α)=-√2/3(π/2
sin(2π-α)-cos(2π+α)=-√2/3
-sinα-cosα=-√2/3, sinα+cosα=√2/3,
二边平方:1+2sinαcosα=2/9, 2sinαcosα=-7/9
(1) π/2<α<π, sinα>0, cosα<0, sinα-cosα>0
sinα-cosα=√(sinα-cosα)²=√(1-2sinαcosα)=√(1-(-7/9))=√(16/9)=4/3
(2) sin^3(2π-α)+cos^3(2π-α)=(-sinα)^3+(cosα)^3=(cosα)^3-(sinα)^3
=(cosα-sinα)(cos^2α+cosαsinα+sin^2α)
=(-4/3)(1-7/18)=(-4/3)*(11/18)=-22/27