在△ABC中,角A满足sin^4A-cos^4A≤cosA-sinA,则(A)0≤A≤π/6(B)0≤A≤π/4(C)π/4≤A≤_数学解答

在△ABC中,角A满足sin^4A-cos^4A≤cosA-sinA,则
(A)0≤A≤π/6
(B)0≤A≤π/4
(C)π/4≤A≤π/3
(D)π/4≤A≤3π/4

人气：474 ℃　时间：2020-05-21 21:57:02

解答

sin^4A-cos^4A=(cos^2A+sin^2A)(cosA+sinA))(sinA-cosA)≤cosA-sinA,得：
由cos^2A+sin^2A=1
得(cosA+sinA))(sinA-cosA)≤cosA-sinA
若cosA-sinA≤0
π/4