[
ewcommand{arccot}{mathrm{arccot}\,}
ewcommand{arcsec}{mathrm{arcsec}\,}
ewcommand{arccsc}{mathrm{arccsc}\,}
ewcommand{d}{mathrm{d}\,}
]
三角函数公式
[egin{aligned}
sin(A+B)&=sin Acos B+cos Asin B\
sin(A-B)&=sin Acos B-cos Asin B\
cos(A+B)&=cos Acos B-sin Asin B\
cos(A-B)&=cos Acos B+sin Asin B\
sin 2A&=2sin Acos A\
cos 2A&=cos^2A-sin^2A=1-2sin^2A=2cos^2A-1\
sinfrac{A}{2}&=sqrt{frac{1-cos A}{2}}\
cosfrac{A}{2}&=sqrt{frac{1+cos A}{2}}\
anfrac{A}{2}&=frac{1-cos A}{sin A}=frac{sin A}{1+cos A}\
sin A+sin B&=2sinfrac{A+B}{2}cosfrac{A-B}{2}\
sin A-sin B&=2cosfrac{A+B}{2}sinfrac{A-B}{2}\
cos A+cos B&=2cosfrac{A+B}{2}cosfrac{A-B}{2}\
cos A-cos B&=-2sinfrac{A+B}{2}sinfrac{A-B}{2}\
an A+ an B&=frac{sin (A+B)}{cos Acos B}\
sin Asin B&=frac{1}{2}[cos(A+B)-cos(A-B)]\
cos Acos B&=frac{1}{2}[cos(A+B)+cos(A-B)]\
sin Acos B&=frac{1}{2}[sin(A+B)+sin(A-B)]\
end{aligned}
]
[frac{a}{sin A}=frac{b}{sin B}=frac{c}{sin C}=2R\
cos A=frac{b^2+c^2-a^2}{2bc}
]
[sin^2A=frac{1-cos 2A}{2}\
cos^2A=frac{1+cos 2A}{2}
]
导数公式
[egin{aligned}
(upm v)'&=u'pm v'\
(uv)'&=u'v+uv'\
(cu)'&=cu'\
(frac{u}{v})'&=frac{u'v-uv'}{v^2}\
c'&=0
end{aligned}
]
[egin{aligned}
(x^n)'&=nx^{n-1}\
(a^x)'&=a^xln x\
(log_ax)'&=frac{1}{xln a}\
(sin x)'&=cos x\
(cos x)'&=-sin x\
( an x)'&=sec^2x\
(cot x)'&=-csc^2x\
(sec x)'&=sec x an x\
(arcsin x)'&=frac{1}{sqrt{1-x^2}}
end{aligned}
]
积分公式
[egin{aligned}
int k d x&=kx+c\
int x^n d x&=frac{1}{n+1}x^{n+1}+c\
int frac{1}{x}d x&=ln |x|+c\
int a^x d x&=frac{a^x}{ln a}+c\
int sin xd x&=-cos x+c\
int cos xd x&=sin x+c\
int sec^2xd x&= an x+c\
int csc^2xd x&=-cot x+c\
int sec x an xd x&=sec x+c\
int cot xcsc xd x&=csc x+c\
int frac{1}{sqrt{1-x^2}}d x&=arcsin x+c\
int frac{1}{1+x^2}d x&=arctan x+c
end{aligned}
]
泰勒展开公式
[f(x)=f(a)+frac{f'(a)}{1!}(x-a)+frac{f''(a)}{2!}(x-a)^2+cdots+frac{f^{(n)}(a)}{n!}(x-a)^n+cdots
]
[frac{1}{1-ax}=sumlimits_{i=0}^infty a^ix^i
]