已知函数y=f(x)的图像关于直线x=3对称,f(-1)=2007且cosα-sinα=(3根号2)/5(1)求u=15sin2α/cos(α+π/4)的值(2)求f(u)的值
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![已知函数y=f(x)的图像关于直线x=3对称,f(-1)=2007且cosα-sinα=(3根号2)/5(1)求u=15sin2α/cos(α+π/4)的值(2)求f(u)的值](/uploads/image/z/1697425-25-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0y%3Df%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%E5%85%B3%E4%BA%8E%E7%9B%B4%E7%BA%BFx%3D3%E5%AF%B9%E7%A7%B0%2Cf%28-1%29%3D2007%E4%B8%94cos%CE%B1-sin%CE%B1%3D%EF%BC%883%E6%A0%B9%E5%8F%B72%EF%BC%89%2F5%EF%BC%881%EF%BC%89%E6%B1%82u%3D15sin2%CE%B1%2Fcos%EF%BC%88%CE%B1%2B%CF%80%2F4%EF%BC%89%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E6%B1%82f%EF%BC%88u%EF%BC%89%E7%9A%84%E5%80%BC)
已知函数y=f(x)的图像关于直线x=3对称,f(-1)=2007且cosα-sinα=(3根号2)/5(1)求u=15sin2α/cos(α+π/4)的值(2)求f(u)的值
已知函数y=f(x)的图像关于直线x=3对称,f(-1)=2007且cosα-sinα=(3根号2)/5
(1)求u=15sin2α/cos(α+π/4)的值
(2)求f(u)的值
已知函数y=f(x)的图像关于直线x=3对称,f(-1)=2007且cosα-sinα=(3根号2)/5(1)求u=15sin2α/cos(α+π/4)的值(2)求f(u)的值
(1) cos(α+π/4)
=√(1/2) * (cosα-sinα)
=(3根号2)/5 * √(1/2)
=3/5
(cosα-sinα)^2 = 1-2sin2α =[(3根号2)/5]^2
即 1-sin2α = 18/25
sin2α = 7/25
u=(15 * 7/25)/(3/5)
=7
(2) y=f(x)的图像关于直线x=3对称
所以 f(6-x)=f(x)
即 f(7)=f(-1)=2007
即 f(u)=2007
u=30sinacosa/cosa-sina=15[1-(cosα-sinα)^2]/cosa-sina