Question

函数f(x)在［-1,1］上满足f(-x)=-f(x)且是减函数,α、β是锐角三角形的两个内角,且α≠β,则下列不等式正确的是

A.f(cosα)＞f(sinβ)                              B.f(sinα)＞f(sinβ)

C.f(cosα)＜f(cosβ)                              D.f(sinα)＜f(sinβ)

Answer 1

答案：A

解析:∵α、β是锐角三角形的两个内角,

∴0＜α＜,0＜β＜,且＜α+β＜π.

∴＞β＞-α＞0.

∴0＜cosβ＜cos(-α)=sinα＜1,

1＞sinβ＞sin(-α)=cosα＞0.

又∵f(x)在［-1,1］上为减函数,

∴f(sinβ)＜f(cosα).