Президентский ФМЛ №239

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

1. $\tg^2{x}+1$
2. $\ctg^2{x}+1$
3. $2\sin{x}\cos{x}$
4. Три формулы $\cos^2{x}-\sin^2{x}$
5. $3\sin{x}-4\sin^3{x}$
6. $4\cos^3{x}-3\cos{x}$
7. $\dfrac{2\tg{x}}{1-\tg^2{x}}$
8. $\sin{x}\cos{y}+\cos{x}\sin{y}$
9. $\sin{x}\cos{y}-\cos{x}\sin{y}$
10. $\cos{x}\cos{y}-\sin{x}\sin{y}$
11. $\cos{x}\cos{y}+\sin{x}\sin{y}$
12. $\dfrac{\tg{x}+\tg{y}}{1-\tg{x}\tg{y}}$
13. $\dfrac{\tg{x}-\tg{y}}{1+\tg{x}\tg{y}}$
14. $\dfrac{1-\cos{2x}}{2}$
15. $\dfrac{1+\cos{2x}}{2}$
16. $\dfrac{2\tg{\dfrac{x}{2}}}{ 1+\tg^2{\dfrac{x}{2}}}$
17. $\dfrac{1-\tg^2{\dfrac{x}{2}}}{1+\tg^2{\dfrac{x}{2}}}$
18. $2\cos{\dfrac{x+y}{2}}\cos{\dfrac{x-y}{2}}$
19. $-2\sin{\dfrac{x+y}{2}}\sin{\dfrac{x-y}{2}}$
20. $2\sin{\dfrac{x+y}{2}}\cos{\dfrac{x-y}{2}}$
21. $2\sin{\dfrac{x-y}{2}}\cos{\dfrac{x+y}{2}}$
22. $\dfrac{1}{2}(\cos{(x-y)}+\cos{(x+y)})$
23. $\dfrac{1}{2}(\cos{(x-y)}-\cos{(x+y)})$
24. $\dfrac{1}{2}(\sin{(x-y)}+\sin{(x+y)})$