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Algebra formulas:

1. (a+B)²= a²+2aB+B²
2. (a+B)²= (a-B)²+4aB
3. (a-B)²= a²-2aB+B²
4. (a-B)²= (a+B)²-4aB
5. a² + B²= (a+B)² - 2aB.
6. a² + B²= (a-B)² + 2aB.
7. a²-B² =(a + B)(a - B)
8. 2(a² + B²) = (a+ B)² + (a - B)²
9. 4aB = (a + B)² -(a-B)²
10. aB ={(a+B)/2}²-{(a-B)/2}²
11. (a + B + C)² = a² + B² + C² + 2(aB + BC + Ca)
12. (a + B)³ = a³ + 3a²B + 3aB² + B³
13. (a + B)³ = a³ + B³ + 3aB(a + B)
14. (a-B)³=a³-3a²B+3aB²-B³
15. a³ + B³ = (a + B) (a² -aB + B²)
16. a³ + B³ = (a+ B)³ -3aB(a+ B)
17. a³ -B³ = (a -B) (a² + aB + B²)
18. a³ -B³ = (a-B)³ + 3aB(a-B)
Sιn0° =0
Sιn30° = 1/2
Sιn45° = 1/√2
Sιn60° = √3/2
Sιn90° = 1
CoS ιS oρρoSιTE oƒ Sιn
Tan0° = 0
Tan30° = 1/√3
Tan45° = 1
Tan60° = √3
Tan90° = ∞
CoT ιS oρρoSιTE oƒ Tan
SEC0° = 1
SEC30° = 2/√3
SEC45° = √2
SEC60° = 2
SEC90° = ∞
CoSEC ιS oρρoSιTE oƒ SEC
2SιnaCoSB=Sιn(a+B)+Sιn(a-B)
2CoSaSιnB=Sιn(a+B)-Sιn(a-B)
2CoSaCoSB=CoS(a+B)+CoS(a-B)
2SιnaSιnB=CoS(a-B)-CoS(a+B)
Sιn(a+B)=Sιna CoSB+ CoSa SιnB.
» CoS(a+B)=CoSa CoSB - Sιna SιnB.
» Sιn(a-B)=SιnaCoSB-CoSaSιnB.
» CoS(a-B)=CoSaCoSB+SιnaSιnB.
» Tan(a+B)= (Tana + TanB)/ (1−TanaTanB)
» Tan(a−B)= (Tana − TanB) / (1+ TanaTanB)
» CoT(a+B)= (CoTaCoTB −1) / (CoTa + CoTB)
» CoT(a−B)= (CoTaCoTB + 1) / (CoTB− CoTa)
» Sιn(a+B)=Sιna CoSB+ CoSa SιnB.
» CoS(a+B)=CoSa CoSB +Sιna SιnB.
» Sιn(a-B)=SιnaCoSB-CoSaSιnB.
» CoS(a-B)=CoSaCoSB+SιnaSιnB.
» Tan(a+B)= (Tana + TanB)/ (1−TanaTanB)
» Tan(a−B)= (Tana − TanB) / (1+ TanaTanB)
» CoT(a+B)= (CoTaCoTB −1) / (CoTa + CoTB)
» CoT(a−B)= (CoTaCoTB + 1) / (CoTB− CoTa)
a/Sιna = B/SιnB = C/SιnC = 2
» a = B CoSC + C CoSB
» B = a CoSC + C CoSa
» C = a CoSB + B CoSa
» CoSa = (B² + C²− a²) / 2BC
» CoSB = (C² + a²− B²) / 2Ca
» CoSC = (a² + B²− C²) / 2Ca
» Δ = aBC/4
» SιnΘ = 0 TEn,Θ = nΠ
» SιnΘ = 1 TEn,Θ = (4n + 1)Π/2
» SιnΘ =−1 TEn,Θ = (4n− 1)Π/2
» SιnΘ = Sιna TEn,Θ = nΠ (−1)^na

1. Sιn2a = 2SιnaCoSa
2. CoS2a = CoS²a − Sιn²a
3. CoS2a = 2CoS²a − 1
4. CoS2a = 1 − Sιn²a
5. 2Sιn²a = 1 − CoS2a
6. 1 + Sιn2a = (Sιna + CoSa)²
7. 1 − Sιn2a = (Sιna − CoSa)²
8. Tan2a = 2Tana / (1 − Tan²a)
9. Sιn2a = 2Tana / (1 + Tan²a)
10. CoS2a = (1 − Tan²a) / (1 + Tan²a)
11. 4Sιn³a = 3Sιna − Sιn3a
12. 4CoS³a = 3CoSa + CoS3a

» Sιn²Θ+CoS²Θ=1
» SEC²Θ-Tan²Θ=1
» CoSEC²Θ-CoT²Θ=1
» SιnΘ=1/CoSECΘ
» CoSECΘ=1/SιnΘ
» CoSΘ=1/SECΘ
» SECΘ=1/CoSΘ
» TanΘ=1/CoTΘ
» CoTΘ=1/TanΘ
» TanΘ=SιnΘ/CoSΘ

. Perimeter Formulas

Square  P=4s 

where  s is the length of the side of the square.

Rectangle  P=2L+2W
   where  L and W are the lengths of the rectangle's sides (length and width).

Triangle  a+b+c
 where    a,b, and c are the side lengths. Right Triangle, with legs a
and b

(see Pythagorean Theorem )
   
P=a+b+a2+b2‾‾‾‾‾‾‾√
    a
and b
are the lengths of the two legs of the triangle

CircleP=C=2πr=πd

   where  r is the radius and d is the diameter.

 
Area Formulas:

Square  A=s2

where  s is the length of the side of the square.

Rectangle A=LW 

where   L and W are the lengths of the rectangle's sides (length and width).

Triangle A=12bh

where b and h are the base and height

Triangle
   
A=s(s−a)(s−b)(s−c)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√wheres=a+b+c2
  

where   a, b , and c are the side lengths and s
is the semiperimeter

Parallelogram A=bh

   where  b is the length of the base and h is the height.

TrapezoidA=b1+b22h
  

where   b1 and b2 are the lengths of the parallel sides and h
the distance (height) between the parallels.

CircleA=πr2

 where  r is the radius.

 
Volume Formulas

CubeV=s3

  where  s is the length of the side.

Right Rectangular PrismV=LWH

 Where   L is the length, W is the width and H
is the height.

Prism or CylinderV=Ah

Where  A is the area of the base, h is the height.

Pyramid or Cone  V=13Ah

 where    A is the area of the base, h is the height.

SphereV=43πr3

where  r is the radius.