已知函数f(x)=(sin2x-cos2x+1)/(2sinx)求f(x)的定义域已知函数f(x)=(sin2x-cos2x+1)/2sinx(1)求f(x)的定义域 (2)设α为锐角,且tanα=4/3,求f(α)的值
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![已知函数f(x)=(sin2x-cos2x+1)/(2sinx)求f(x)的定义域已知函数f(x)=(sin2x-cos2x+1)/2sinx(1)求f(x)的定义域 (2)设α为锐角,且tanα=4/3,求f(α)的值](/uploads/image/z/763136-8-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D%28sin2x-cos2x%2B1%29%2F%282sinx%29%E6%B1%82f%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%EF%BC%88sin2x-cos2x%2B1%EF%BC%89%2F2sinx%281%29%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F+%282%29%E8%AE%BE%CE%B1%E4%B8%BA%E9%94%90%E8%A7%92%2C%E4%B8%94tan%CE%B1%3D4%2F3%2C%E6%B1%82f%28%CE%B1%29%E7%9A%84%E5%80%BC)
已知函数f(x)=(sin2x-cos2x+1)/(2sinx)求f(x)的定义域已知函数f(x)=(sin2x-cos2x+1)/2sinx(1)求f(x)的定义域 (2)设α为锐角,且tanα=4/3,求f(α)的值
已知函数f(x)=(sin2x-cos2x+1)/(2sinx)求f(x)的定义域
已知函数f(x)=(sin2x-cos2x+1)/2sinx
(1)求f(x)的定义域
(2)设α为锐角,且tanα=4/3,求f(α)的值
已知函数f(x)=(sin2x-cos2x+1)/(2sinx)求f(x)的定义域已知函数f(x)=(sin2x-cos2x+1)/2sinx(1)求f(x)的定义域 (2)设α为锐角,且tanα=4/3,求f(α)的值
1.sinx≠0,∴ x≠kπ.∴f(x)的定义域为{x|x≠kπ,k∈Z}
2.f(x)=(sin2x-cos2x+1)/(2sinx)
=(2sixcosx+2sin²x)/(2sinx)
=cosx+sinx
α为锐角,∴sinα>0,cosα>0.
∵tanα=4/3,
sin²α+cos²α=1
sinα/cosα=4/3
解方程组得sinα=4/5 cosα=3/5
f(α)=2sinα+2cosα=7/5
(1)、sinx不=0,所以x不=kπ;
(2)、f(x)={2sinxcosx-[1-2(sinx)^2]+1}=2sinx(cosx+sinx)/2sinx=cosx+sinx;,
由tanα=4/3,构造直角三角形,可以直接得出:sinα=4/5,cosα=3/5,所以f(α)=7/5
1. sinx≠0 x≠kπ
2. f(x)=(sin2x-cos2x+1)/(2sinx)
=(2sixcosx-1+2sin^2x+1)/2sinx
=cosx+sinx
α为锐角,且tanα=4/3, sina=4/5 cosa=3/5
f(a)=2sina+2cosa=7/5