Question

数学难题求教

Answer 1

解:由.sin(π-α)-cos(π+α)=√2/3 (π/2＜α＜π)得

sinα+cosα=√2/3
(奇变偶不变，正负看象限。)

所以，(sinα+cosα)^2=(√2/3)^2=2/9①

又有(sinα)^2+(cosα)^2=1②

①-②式得，2sinαcosα=-7/9③

①-2×③得
(sinα-cosα)^2=16/9

sinα-cosα=4/3
(因为 π/2＜α＜π ，所以sinα＞cosα)

追答

sin³(2π-α)+cos³(2π-α)
=sin³(-α)+cos³(α)
=cos³α-sin³α
=(cosα-sinα)(cos²α+cosαsinα+sin²α)
=-4/3×(1+√3/2)
=-4/3-2√3/3

Answer 2

先用立方差公式展开，再求已知和化一公式联立求出两个之积带去就行了

Answer 3

1题应该是3分之根号2

Answer 4

找百度

Answer 5

我是学渣