sin3xcos2x积化和差

毋狄府4166高一三角 sinx+sin5x+sin3x=0 -
卓朋高13487212905 ______ sin(3x-2x)+sin(3x+2x)+sin3x → sin3xcos2x-cos3xsin2x+sin3xcos2x+cos3xsin2x+sin3x → sin3xcos2x+sin3xcos2x+sin3x → 2sin3xcos2x+sin3x → 2cos2x(sin3x) ∴2cos2x=0或sin3x=0

毋狄府4166cos3xcos2x求积分的详解 -
卓朋高13487212905 ______ cos3xcos2x=1/2[cos5x+cosx] 所以, ∫cos3xcos2xdx=1/2*∫(cos5x+cosx)dx =1/10*sin5x+1/2*sinx+C C表示任意常数

毋狄府4166sin3xcos2xdx的不定积分为多少 -
卓朋高13487212905 ______[答案] 先做积化和差: 2sin3x*cos2x=sin5x+sinx 下面就简单了,直接化为正弦函数的积分

毋狄府4166求解不定积分∫ xsin3xcosx dx -
卓朋高13487212905 ______[答案] 提供思路:先将sin3xcosx积化和差,分成两个积分,然后用分部积分法,计算. 结果:(1/2)(-(1/2)xcos2x+(1/4)sin2x)+ (1/2)(-(1/4)xcos4x+(1/16)sin4x)+C

毋狄府4166为什么sin2xcos3x=(sin5x - sinx)/2,各位仁兄能说说吗?不胜感谢! -
卓朋高13487212905 ______ 根据公式sinacosb=1/2(sin(a+b)+sin(a-b))得 sin2xcos3x=1/2(sin(2x+3x)+sin(2x-3x)) =1/2(sin5x+sin(-x)) =(sin5x-sinx)/2

毋狄府4166(sin4X+sinX)/sin4X=sin3X/sin2x化成sin4X+sinX=2sin3xcos2x -
卓朋高13487212905 ______ sin4x=2sin2xcos2x (sin4X+sinX)/sin4X=(sin4X+sinX)/(2sin2xcos2x)=sin3X/sin2x 所以sin4X+sinX=(sin3X/sin2x)*(2sin2xcos2x)=2sin3xcos2x 望采纳,谢谢

毋狄府4166各位数学高手,“sin3x.sinx”怎么化到“1/2(cos2x - cos4x)”啊?教教我吧!
卓朋高13487212905 ______ sin3xsinx=sin(2x+x)sinx=(sin2xcosx+cos2xsinx)sinx=sin2xsinxcosx+cos2xsinxsinx=sin2xsin2x/2+cos2x*(1-cos2x)/2=(sin2xsin2x-cos2xcos2x)/2+cos2x/2=(cos2x-cos4x)/2

毋狄府4166求证sin3xsin^3x+cos3xcos^3x=cos^3 2x 求详解 -
卓朋高13487212905 ______ sin3xsin^3x+cos3xcos^3x=cos^3(2x) 证明:左侧=sin(x+2x)sin^3x+cos(x+2x)cos^3x =sin^4xcos2x+sin2xcosxsin^3x+cos^4xcos2x-sinxcos^3xsin2x =sin^4xcos2x+2sin^4xcos^2x+cos^4xcos2x-2sin^2xcos^4x =cos2x(sin^4x+cos^4x)+2sin^2xcos^2x(sin^2x-cos^2x) =cos2x(sin^4x+cos^4x-2sin^2xcos^2x) =cos2x(sin^2x-cos^2x)^2 =cos^3(2x) =右侧

毋狄府4166求y=sin3x*sin2x的n阶导数 -
卓朋高13487212905 ______[答案] y(1)=6cos3xcos2x y(2)=6^2*sin3xsin2x ∴n是奇数时,y(n)=6^n*cos3xcos2x; n是偶数时,f(n)=6^n*sin3xcos2x

毋狄府4166根号3sin2x +cos 2x的化简过程 -
卓朋高13487212905 ______ √3sin2x+cos2x =2(√3/2sin2x+1/2cos2x) =2(sin2xcosπ/6+cos2xsinπ/6) =2sin(2x+π/6)