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

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