Everyone has a different opinion.

Extension: the sum of the first n terms of some series.

1+2+3+4+5+6+7+8+9+.+n = n(n+ 1)/2+3+5+7+9+ 1 1+| 3+ 15+…+(2n- 1)= N2

2+4+6+8+ 10+ 12+ 14+…+(2n)= nln+l)

12+22+32+42+52+62+72+82+..+n2=nln+ 1)(2n+ 1)/6

13+23+33+43+53+63+n3 = N2(n+ 1)2/4

*2+2*3+3*4+4*5+5*6+6*7+.+nln+l)=nln+ 1)(n+2)/3

Sine theorem a/sinA=b/sinB=clsinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.

Cosine Theorem 62=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..

The arc length formula l=a*ra is the radian number r > of the central angle; 0 sector area formula s= 1/2*l*r

Multiplication and factorization a2-62 = (a+b) la-b) a3+63 = (a+b) la2-ab+62) a3-63 = (a-bla2+ab+62).

Trigonometric inequality | a+b | < la |+| bl la-bl <; la |+| bl lal≤b & lt； = & gt-b≤a≤b

la-bl ≥ lal-Ibl -lal ≤ a ≤ lal

Solution of the quadratic equation in one variable -6+√(62-4ac)/2a-b-√(b2-4ac)/2a Relationship between roots and coefficients XI+X2=-6/aXI*X2=c/a Note: Vieta's theorem.

discriminant

62-4ac=0 Note: The equation has two equal real roots.

62-4ac >0 Note: The equation has two unequal real roots.

62-4ac & lt； Note: The equation has no real root, but a complex number of the yoke.

Reduced power formula

(sin2)x= 1-cos2x/2

(cos2)x=i=cos2x/2

General formula of trigonometric function

Let tanla/2)=t

sina=2t/ll+t^2)

cosa=(l-t^2)/l 1+t^2)

Tana = 2t/l 1-t 2).

Two-angle sum formula

sinlA+B)= Sina cosb+cosa sin(A-B)= Sina cosb-sinBcosAcoslA+B)= cosa cosb-Sina sinb coslA-B)= cosa cosb+Sina sinb

tan(A+B)=(tanA+tanB)/ll-tanA tanB)tanlA-B)=(tanA-tanB)/ll+tanA tanB)

ctglA+B)= lctgActgB- 1)/lctgB+ctgA)ctglA-B)=(ctgActgB+ 1)/lctgB-ctgA)

Double angle formula

tan2A = 2 tana/ll-tan2A)ctg2A = lctg2A- 1)/2 ctga

cosia = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a

half-angle formula

sinlA/2)= √( ll-cosA)/2)sinlA/2)=-√ll-cosA)/2)

coslA/2)=√lll+cosA)/2)cos(A/2)=-√lll+cosA)/2)

tan(A/2)=√lll-cosA)/lll+cosA))tan la/2)=-√lll-cosA)/lll+cosA))

ctglA/2)=√lll+cosA)/lll-cosA))ctglA/2)=-√lll+cosA)/lll-cosA))

Sum difference product

2 Sina cosb = sinlA+B)+sinlA-B)2 cosa sinb = sinlA+B)-sinlA-B)