Question

已知函数f(x)=1-根号2sin(2x-π/4）/cosx

1）求F(X)的定义域 2）设a是第四象限的角，切tana=4/3求F（a)的值 过程谢谢～～～

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.