Multiplication and factorization
a2-B2 =(a+b)(a-b)a3+B3 =(a+b)(a2-a b+B2)a3-B3 =(a-b)(a2+a b+B2)
Triangle inequality
| a+b |≤| a |+| b | | a-b |≤| a |+| b | | a |≤b & lt; = & gt-b≤a≤b
|a-b|≥|a|-|b| -|a|≤a≤|a|
Solution of quadratic equation in one variable
-b+√(B2-4ac)/2a-b-b+√(B2-4ac)/2a
Relationship between root and coefficient
X1+x2 =-b/ax1* x2 = c/a note: Vieta's theorem.
Discriminant b2-4a=0 Note: The equation has two equal real roots.
B2-4ac >0 Note: The equation has real roots.
B2-4ac & lt; 0 Note: The equation has multiple yokes.
formulas of trigonometric functions
Two-angle sum formula
sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinb cosa
cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
Double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
half-angle formula
sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
What edition is this book of yours?