Question

己知函数f（x）=1-√2sin（2π,-π /4）/cosx（1）求f（x）定义域。（2）设α是第

己知函数f（x）=1-√2sin（2π,-π
/4）/cosx（1）求f（x）定义域。（2）设α是第四象限的角且tanα=-4/3求f（α）的值

Answer 1

1).cosx≠0.
x≠kπ+π/2.k∈Z.
∴f(x)的定义域为{x│x≠kπ+π/2.k∈Z}.

2)α是第四象限的角，切tanα=-4/3.
sinα=-4/5, cosα=3/5.
sin2α=2sinαcosα=-24/25.
cos2α=2cos^2-1=-7/25.
√2sin(2x-π/4）=√2(sin2xcosπ/4-cos2xsinπ/4)
=sin2x-cos2x
=-17/25.
∴f(α)=1-(-17/25)/(3/5) =32/15.