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tAnx sinx

sinx=tanx*cosx=tanx*根号(1-cosx的平方)secx=1/cosx=1/根号(1-sinx的平方)

tanx = sinx / cosx x->0 时 tanx 与sinx 是等价无穷小

tanx=y/x(tanx)^2=y^2/x^21/(tanx)^2=x^2/y^21/(tanx)^2+1=1+x^2/y^2=(x^2+y^2)/y^2=r^2/y^2=(1/sinx)^2∴1/【1/(tanx)^2+1】=(sinx)^2sinx=√{1/【1/(tanx)^2+1】}

tanx-sinx=sinx(1-cosx)/cosx=1/2x

1-cos ^2x=sin^2x 方程两边同时乘以sinx^2/cosx^2sin^2x/cos^2x - sin^2x =sin^2x sin^2x/cos^2xtan^2x -sin^2x =sin^2 x tan^2 x(tanx-sinx)(tanx+sinx)=(sinx tanx) (sinx tanx)divide both sides by sinxtanx/(ta

lim(x→0)(tanx-sinx)/(sinx)^3=lim(x→0)tanx(1-cosx)/x^3=lim(x→0)x*(1/2x^2)/x^3=1/2

画一下图就知道了,有可能相等,有可能tanx大于sinx,有可能小于.

用万能公式代换tanx=2tan(x/2)/[1-tan^2(x/2)]sinx=2tan(x/2)/[1+tan^2(x/2)]∫1/(tanx+sinx)dx=∫[1+tan^2(x/2)][1-tan^2(x/2)]/[tan(x/2)]dx然后展开就有结果了

20 y = (x-tanx)sinx 利用:y = u(x)v(x) y'= u'v + uv'y'= (1-secx)sinx + (x-tanx)cosx= xcosx - tanx secx

y=tanx+sinx=sinx/cosx+sinx=sinx(1+1/cosx)cosx≠0,x≠2kπ+π/2且x≠2kπ-π/2即:x≠(2k+1)π/2(其中k=0,±1,±2)∴y=tanx+sinx的定义域为{x|x≠(2k+1)π/2,k=0,±1,±2}

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