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1, multiplication and factorization a2-B2 = (a+b) (a-b) a3+B3 = (a+b) (a2-ab+B2) a3-B3 = (a-b (a2+ab+B2))
2. Trigonometric inequality | A+B |≤| A |+B ||||||| A |+B|| A |≤ B < = >-B≤ A ≤ B | A-B |≥| A |-B| | A |≤
3. The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a.
The sum formula of two angles of trigonometric function;
4、sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinBcosA
5、cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
6、tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
7、ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
8. The angle doubling formula tan2a = 2tana/(1-tan2a) ctg2a = (ctg2a-1)/2ctga.
9、cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
10, and the half-angle formula sin (a/2) = √ ((kloc-0/-COSA)/2) sin (a/2) =-√ ((1-COSA)/2).
1 1、cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
12、tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
13、ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
Sum difference product
14、2 Sina cosb = sin(A+B)+sin(A-B)2 cosa sinb = sin(A+B)-sin(A-B)
15、2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)
16、sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)
17、tanB = sin(A+B)/cosAcosB tanA-tanB = sin(A-B)/cosAcosB
18、ctgA+ctgBsin(A+B)/Sina sin B- ctgA+ctgBsin(A+B)/Sina sinb