Multiplication and Factorization of Common Mathematical Formulas

Answer? -B? =(a+b)(a-b) a？ +b？ =(a+b)(a？ -ab+b？ )a？ -B? =(a-b)(a？ +ab+b？ ) trigonometric inequality

a+b |≤| a |+| b | | a-b |≤| a |+| b | | a |≤b & lt； =>-b ≤ a ≤ b | a-b |≥| a |-b | | a |≤ a ≤| the solution of a quadratic equation.

-b+√(b？ -4ac)/2a -b-√(b？ The relationship between -4ac)/2a root and coefficient (Vieta theorem) X1+x2 =-b/ax1* x2 = c/a discriminant.

b？ -4ac=0 Note: The equation has two equal real roots b? -4ac & gt； 0 note: the equation has two unequal real roots b? -4ac & lt； Note: the equation has no real root, but there is a formula for the sum of the formulas of two angles of trigonometric function with a yoke.

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-65433)

Tan? A=2tanA/( 1-tan？ A) ctg？ A=(ctg？ A- 1)/2ctga cos？ a=cos？ Sin. a=2cos？ a- 1= 1-2sin？ 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))。

2 Sina cosb = sin(A+B)+sin(A-B)2 cosa sinb = sin(A+B)-sin(A-B)2 cosa cosb = cos(A+B)-sin(A-B)-2 Sina sinb = cos(A+B)-cos(A-B)

Sina+sinb = 2 sin ((a+b)/2) cos ((a-b)/2 COSA+COSB = 2 COS ((a+b)/2) SIN ((a-b)/2) Tana +TANB = SIN (a+b)/COSA COS.

1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2 1+3+5+7+9+ 1 1+ 13+ 15+…+(2n- 1)= n？

2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6 13+23+33+43

1* 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n (n+1) = n (n+1) (n+2)/3 sine theorem.

A/sinA=b/sinB=c/sinC=2R Note: where r stands for the cosine theorem of the radius of the circumscribed circle of a triangle.

b？ =a？ +c？ -2accosB Note: Angle b is the included angle between side A and side C..

I hope it will be helpful to your study.

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