15.已知sin(x/2)-2cos(x/2)=0.(1)求tanx的值;(2)求[√2 cos([π/4]+x)×sinx]/(cos2x)的值.16.已知函数f(x)=x^3-(1+b)x^2+bx,b∈R.(1)若函数f(x)在点(1,f(1))处的切线与直线x+y-3=0平行,求b的值;(2)在(1)的条件
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![15.已知sin(x/2)-2cos(x/2)=0.(1)求tanx的值;(2)求[√2 cos([π/4]+x)×sinx]/(cos2x)的值.16.已知函数f(x)=x^3-(1+b)x^2+bx,b∈R.(1)若函数f(x)在点(1,f(1))处的切线与直线x+y-3=0平行,求b的值;(2)在(1)的条件](/uploads/image/z/14163239-47-9.jpg?t=15.%E5%B7%B2%E7%9F%A5sin%28x%2F2%29-2cos%28x%2F2%29%3D0.%281%29%E6%B1%82tanx%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82%5B%E2%88%9A2+cos%28%5B%CF%80%2F4%5D%2Bx%29%C3%97sinx%5D%2F%28cos2x%29%E7%9A%84%E5%80%BC.16.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%5E3-%281%2Bb%29x%5E2%2Bbx%2Cb%E2%88%88R.%EF%BC%881%EF%BC%89%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E7%82%B9%281%2Cf%281%29%29%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E4%B8%8E%E7%9B%B4%E7%BA%BFx%2By-3%3D0%E5%B9%B3%E8%A1%8C%2C%E6%B1%82b%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%882%EF%BC%89%E5%9C%A8%EF%BC%881%EF%BC%89%E7%9A%84%E6%9D%A1%E4%BB%B6)
15.已知sin(x/2)-2cos(x/2)=0.(1)求tanx的值;(2)求[√2 cos([π/4]+x)×sinx]/(cos2x)的值.16.已知函数f(x)=x^3-(1+b)x^2+bx,b∈R.(1)若函数f(x)在点(1,f(1))处的切线与直线x+y-3=0平行,求b的值;(2)在(1)的条件
15.已知sin(x/2)-2cos(x/2)=0.
(1)求tanx的值;(2)求[√2 cos([π/4]+x)×sinx]/(cos2x)的值.
16.已知函数f(x)=x^3-(1+b)x^2+bx,b∈R.
(1)若函数f(x)在点(1,f(1))处的切线与直线x+y-3=0平行,求b的值;
(2)在(1)的条件下,求f(x)在区间[0,3]上的最值.
画表格用文字
15.已知sin(x/2)-2cos(x/2)=0.(1)求tanx的值;(2)求[√2 cos([π/4]+x)×sinx]/(cos2x)的值.16.已知函数f(x)=x^3-(1+b)x^2+bx,b∈R.(1)若函数f(x)在点(1,f(1))处的切线与直线x+y-3=0平行,求b的值;(2)在(1)的条件
15.(1)
∵sin(x/2)-2cos(x/2)=0.
∴tan(x/2)=2
∴tanx=2tan(x/2)/[1-tan²(x/2)]=4/(1-4)=-4/3
(2)[√2 cos([π/4]+x)×sinx]/(cos2x)
=[√2(cosx*√2/2-sinx*√2/2)×sinx]/cos2x
=(cosx-sinx)sinx /(cos²x-sin²x)
=(cosx-sinx)sinx/[(cosx-sinx)(cosx+sinx)]
=sinx/(cosx+sinx)
=tanx/(1+tanx)
=(-4/3)/(1-4/3)
=4
16.
(1) .
f'(x)=3x^2-2(1+b)x+b
∵函数f(x)在点(1,f(1))处的切线与直线x+y-3=0平行
∴f'(1)=-1 即 3-2(1+b)+b=-1 ∴b=2
(2)f'(x)=3x^2-6x+2 =3(x-1)² ,
f'(x)=0 3x^2-6x+2=0
x1=(3-√2)/3, x1=(3+√2)/3,
系数不配合