由倍角公式cos2x=2cos^2x-1,可知cos2x可以表示为cosx的二次多项式.对于cos3x,我们有cos3x=cos(2x+x)=cos2xcosx-sin2xsinx=(2cos^2x-1)cosx-2(sinxcosx)sinx=2cos^3x-cosx-2(1-cos^2x)cosx=4cos^3x-3cosx.可见cos3x可以表示为cosx的三次多项式.一般地,存在一个n次多项式P_n(t),使得cosnx=P...
若a,b,c,d为实数,且sin x √3 cos x=ad-bc,定义函数 f(x)=,现2cos x2cos x将f(x)的图象先向左平移 (5π)/(12) 个单位,再向上平移 √3 个单位后得到函数g(x)的图象,则g(x)的解析式为 g(x)=2cos2x .16.已知 f(x)=sin(3x+\varphi)(|\varphi|π/(2)) 为奇函数,若对任...
If x= cos 10^(@)cos 20^(@) cos 40^(@), then the value of x is 04:54 (iv)यदि cos(40^(@)+x)=sin30^(@) 02:01 If tanx=sin45^(@)*cos45^(@)+sin30^(@) If so x Find the value of 01:10 In the following x Find the value of (i) If tan3x=sin45^(@)*...
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sin3x+cos3x=(sinx+cosx)(sin2x−sinxcosx+cos2x)=(sinx+cosx)(1−sinxcosx)=(sinx+cosx)[1...
(1)lim_(x→π)sin3x=0.1imtan5x=0∴为0/0=∴lim_(x→∞)(sin3x)/(sin5x)=lim_(x→∞)(3cos3x)/(1/(cos^2x))=(-3)/(3/1)=-3/5(2)lim_(x→+∞)1n(e^x+1)=∞⋅lime^x=∞∴为∞/(∞)∴lim_(x→∞)(ln(e^x+1))/(e^x)=lim_(x→+∞)(e^x+1)/(e^x)=li...
首先必须把解析式化简,而化简解析式需要运用众多的三角公式使之变形,其中包括积化和差与和差化积.解: sin 3.x sin3x + cos 3.x cos3x = (sin 3.x sin x) sin2rx +(cos 3.x cos x)cos2x=1/2[(cos2x-cos4x)sin^2x+(cos2x+cos4x)cos^2x] =1/2[(sin^2x+cos^2x)cos2x+(cos^2x-sin...
=2cos3x-cosx-2(1-cos2x)cosx=4cos3x-3cocs.可见cos3x可以表示为cosx的三次多项式.一般地,存在一个n次多项式Pn(t),使得cosnx=Pn(cosx),这些多项式Pn(t)称为切比雪夫(P.L.Tschebyscheff)多项式.(1)请尝试求出P4(t),即用一个cosx的四次多项式来表示cos4x....
记展开式为sinx=a0+a1x+a2x2+a3x3+a4x4+a5x5+...由sin0=0=a0，可得a0=0。求导得(sinx)′=cosx=a1+2a2x+3a3x2+4a4x3+5a5x4+...由cos0=1=a1，可得a1=1。继续求导(cosx)′=−sinx=2a2+3⋅2a3x+4⋅3a4x2+5⋅4a5x3+...再由−sin0=0=2a2，可得a2=0。继续求导(−sinx)′=...
Answer to: Calculate the limit of each expression as x approaches infinity. A) cos(3x)/(5x - 1) B) (4 + x*sin(x))/(2x - 3) By signing up, you'll...