Формули елементарної математики

Степені

$a^{m}\cdot a^{n}=a^{m+n}$ ;
${\frac {a^{m}}{a^{n}}}=a^{m-n}$ ;
$(a\cdot b)^{n}=a^{n}\cdot b^{n}$ ;
$(a^{m})^{n}=a^{m\cdot n}$ ;
$a^{-n}={\frac {1}{a^{n}}}$ .

Тригонометрія

$\sin \alpha =\cos(90^{\circ }-\alpha )$ ;
$\operatorname {tg} \alpha =\operatorname {ctg} (90^{\circ }-\alpha )$ ;
$\sin ^{2}\alpha +\cos ^{2}\alpha =1$ ;
$\operatorname {tg} \alpha ={\frac {\sin \alpha }{\cos \alpha }}$ ;
$\operatorname {ctg} \alpha ={\frac {\cos \alpha }{\sin \alpha }}$ ;
$\operatorname {tg} \alpha \cdot \operatorname {ctg} \alpha =1$ ;
$1+\operatorname {tg} ^{2}\alpha ={\frac {1}{\cos ^{2}\alpha }}$ ;
$1+\operatorname {ctg} ^{2}\alpha ={\frac {1}{\sin ^{2}\alpha }}$ ;
$\sin 2\alpha =2\sin \alpha \cos \alpha$ ;
$\cos 2\alpha =\cos ^{2}\alpha -\sin ^{2}\alpha$ ;
$\sin 3\alpha =3\sin \alpha -4\sin ^{3}\alpha$ ;
$\cos 3\alpha =4\cos ^{3}\alpha -3\cos \alpha$ .

Логарифм

$\log _{a}(m\cdot n)=\log _{a}m+\log _{a}n$ ;
$\log _{a}(m/n)=\log _{a}m-\log _{a}n$ ;
$\log _{a}(n^{k})=k\cdot \log _{a}n$ .

Див. також

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