Президентский ФМЛ №239

Это старая версия документа!

$\DeclareMathOperator{\tg}{tg}$ $\DeclareMathOperator{\ctg}{ctg}$

$\sin{2x} = 2\sin{x}\cos{x}$
Три формулы $\cos{2x}=\cos^2{x}-\sin^2{x}$
$\sin{3x}=3\sin{x}-4\sin^3{x}$
$\cos{3x}=4\cos^3{x}-3\cos{x}$
$\tg{2x}=\dfrac{2\tg{x}}{1-\tg^2{x}}$
$\sin{(x+y)}=\sin{x}\cos{y}+\cos{x}\sin{y}$
$\sin{(x-y)}=\sin{x}\cos{y}-\cos{x}\sin{y}$
$\cos{(x+y)}=\cos{x}\cos{y}-\sin{x}\sin{y}$
$\cos{(x-y)}=\cos{x}\cos{y}+\sin{x}\sin{y}$
$\tg{(x+y)}=\dfrac{\tg{x}+\tg{y}}}{1-\tg{x}\tg{y}}$
$\tg{(x-y)}=\dfrac{\tg{x}-\tg{y}}}{1+\tg{x}\tg{y}}$
$\sin^2{x}=\dfrac{1-\cos{2x}}{2}$
$\cos^2{x}=\dfrac{1+\cos{2x}}{2}$
Универсальная подстановка $\sin{x}=\dfrac{2\tg{\dfrac{x}{2}}}{ 1+\tg^2{\dfrac{x}{2}}}$
Универсальная подстановка $\cos{x}=\dfrac{2\tg{1-\tg{\dfrac{x}{2}}}}{1+\tg^2{\dfrac{x}{2}}}$
$\cos{x}+\cos{y}$
$\cos{x}-\cos{y}$
$\sin{x}+\sin{y}$
$\sin{x}-\sin{y}$
$\cos{x}\cos{y}$
$\sin{x}\sin{y}$
$\sin{x}\cos{y}$
$\dfrac{1}{\cos^2{x}}$
$\dfrac{1}{\sin^2{x}}$
$\sin{(\pi-x)}$
$\sin{(\pi+x)}$
$\sin{\left(\dfrac{\pi}{2}-x\right)}$
$\sin{\left(\dfrac{\pi}{2}+x\right)}$
$\sin{\left(\dfrac{3\pi}{2}-x\right)}$
$\sin{\left(\dfrac{3\pi}{2}+x\right)}$
$\sin{(-x)}$
$\cos{(\pi-x)}$
$\cos{(\pi+x)}$
$\cos{\left(\dfrac{\pi}{2}-x\right)}$
$\cos{\left(\dfrac{\pi}{2}+x\right)}$
$\cos{\left(\dfrac{3\pi}{2}-x\right)}$
$\cos{\left(\dfrac{3\pi}{2}+x\right)}$
$\cos{(-x)}$
$\tg{(\pi-x)}$
$\tg{(\pi+x)}$
$\tg{\left(\dfrac{\pi}{2}-x\right)}$
$\tg{\left(\dfrac{\pi}{2}+x\right)}$
$\tg{\left(\dfrac{3\pi}{2}-x\right)}$
$\tg{\left(\dfrac{3\pi}{2}+x\right)}$
$\tg{(-x)}$
$\ctg{(\pi-x)}$
$\ctg{(\pi+x)}$
$\ctg{\left(\dfrac{\pi}{2}-x\right)}$
$\ctg{\left(\dfrac{\pi}{2}+x\right)}$
$\ctg{\left(\dfrac{3\pi}{2}-x\right)}$
$\ctg{\left(\dfrac{3\pi}{2}+x\right)}$
$\ctg{(-x)}$