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Соотношение между функциями

1. sin x = (2tg x/2)/(1+tg²x/2)
2. cos x = (1-tg²*2/x)/(1+tg²*x/2)
3. sin2x = (2tg x)/(1+tg²*x)
4. sin²α = 1/(1+ctg²α) = tg²α/(1+tg²α)
5. cos²α = 1/(1+tg²α) = ctg²α/(1+ctg²α)
6. ctg2α = (ctg²α-1)/2ctg α
7. sin3α = 3sin α- 4sin³α = cos²α*sin α-sin³α
8. cos3α = 4cos³α-3cos α = cos³α-3cos α*sin²α
9. tg3α = (3tg -tg³α)/(1-3tg²α)
10. ctg3α = (ctg³α-3ctg α)/(3ctg²α-1)
11. sin α/2 = ±√((1-cos α)/2)
12. cos α/2 = ±√((1+cos α)/2)
13. tg α/2 = ±√((1-cos α)/(1+cos α)) = sin α/(1-cos α) = (1+cos )/sin α
14. ctg α/2 = ±√((1+cos α)/(1-cos α)) = sin α/(1+cos α) = (1-cos )/sin α
15. sin(arcsin α) = α
16. cos(arccos α) = α
17. tg(arctg α) = α
18. ctg(arcctg α) = α
19. arcsin(sin α) = α ; α∈[-π/2 ; π/2]
20. arccos(cos α) =  α ; α∈[0 ; π]
21. arctg(tg α) =  α; α∈[-π/2 ; π/2]
22. arcctg(ctg α) =  α ; α∈[0 ; π]

arccos(cos α) =

1. a-2πk; α∈[2πk ; (2k+1)π]
2. 2πk-α; α∈[(2k+1)π ; 2πk]

arcsin(sin α) = 

1. a-2πk; α∈[-π/2+2πk ; π/2+πk]
2. (2k+1)π-α; α∈[π/2+2πk ; 3π/2+πk]

arctg(tg α) = α-πk

1. α∈[-π/2+πk ; π/2+πk]

arctg(tg α) = α-πk

1. α∈[πk ; (k+1)π]

1. arcsin α = -arcsin(-α) = π/2 -arccos α = arctg α/√(1-a²)
2. arccos α = π-arccos(-α) = π/2 -arcsin α = arcctg α/√(1-a²)
3. arctg α = -arctg(-α) = π/2 -arcctg α = arcsin α/√(1+a²)
4. arcctg α = π-arccctg(-α) = -arccos α = arccos α/√(1-a²)
5. arctg α = -arctg 1/α = π/2 -arcsin α/√(1+a²) = arccos 1/√(1+a²)

1. arcsin α + arccos = π/2
2. arcctg α + arctg α = π/2