Comprehensive list of basic MATH formulas ..!!!

ALGEBRIC IDENTITIES :

 (a+b+c)²= a²+b²+c²+2(ab+bc+ca)

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= f(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)

Trigonometric Identities :

Sin0° =0

Sin30° = 1/2

Sin45° = 1/√2

Sin60° = √3/2

Sin90° = 1

Cos is opposite of Sin

tan0° = 0

tan30° = 1/√3

tan45° = 1

tan60° = √3

tan90° = ∞

Cot is opposite of tan

Sec0° = 1

Sec30° = 2/√3

Sec45° = √2

Sec60° = 2

Sec90° = ∞

Cosec is opposite of Sec

2(Sin a)(Cos b)=Sin(a+b)+Sin(a-b)

2(Cos a)(sin b)=Sin(a+b)-Sin(a-b)

2(Cos a)(Cos b)=Cos(a+b)+Cos(a-b)

2(Sin a)(sin b)=Cos(a-b)-Cos(a+b)

Sin(a+b)=(Sin a)(Cos b)+(Cos a)(sin b).

» Cos(a+b)=(Cos a)(Cos b) - (Sin a)(sin b).

» Sin(a-b)=(Sin a)(Cos b)-(Cos a)(sin b).

» Cos(a-b)=(Cos a)(Cos b)+(Sin a)(sin b).

» tan(a+b)= ((tan a) + (tan b))/ (1−(tan a)(tan b))

» tan(a−b)= ((tan a) − (tan b)) / (1+ (tan a)(tan b))

» Cot(a+b)= ((Cot a)(Cot b) −1) / ((Cot a) + (Cot b))

» Cot(a−b)= ((Cot a)(Cot b) + 1) / ((Cot b)− (Cot a))

» Sin(a+b)=(Sin a)(Cos b)+ (Cos a)(sin b).

» Cos(a+b)=(Cos a)(Cos b) +(Sin a)(sin b).

» Sin(a-b)=(Sin a)(Cos b)-(Cos a)(sin b).

» Cos(a-b)=(Cos a)(Cos b)+(Sin a)(sin b).

» tan(a+b)= ((tan a) + (tan b))/ (1−(tan a)(tan b))

» tan(a−b)= ((tan a) − (tan b)) / (1+ (tan a)(tan b))

» Cot(a+b)= ((Cot a)(Cot b) −1) / ((Cot a) + (Cot b))

» Cot(a−b)= ((Cot a)(Cot b) + 1) / ((Cot b) − (Cot a))

a/(Sin a) = b/(sin b) = c/Sinc = 2r

» a = b Cosc + c (Cos b)

» b = a Cosc + c (Cos a)

» c = a (Cos b) + b (Cos a)

» (Cos a) = (b² + c²− a²) / 2bc

» (Cos b) = (c² + a²− b²) / 2ca

» Cosc = (a² + b²− c²) / 2ca

» Δ = abc/4r

» SinΘ = 0 then,Θ = nΠ

» SinΘ = 1 then,Θ = (4n + 1)Π/2

» SinΘ =−1 then,Θ = (4n− 1)Π/2

» SinΘ = (Sin a) then,Θ = nΠ (−1)^na

1. Sin2a = 2(Sin a)(Cos a)

2. Cos2a = Cos²a − Sin²a

3. Cos2a = 2Cos²a − 1

4. Cos2a = 1 − 2Sin²a

5. 2Sin²a = 1 − Cos2a

6. 1 + Sin2a = ((Sin a) + (Cos a))²

7. 1 − Sin2a = ((Sin a) − (Cos a))²

8. tan2a = 2(tan a) / (1 − tan²a)

9. Sin2a = 2(tan a) / (1 + tan²a)

10. Cos2a = (1 − tan²a) / (1 + tan²a)

11. 4Sin³a = 3(Sin a) − Sin3a

12. 4Cos³a = 3(Cos a) + Cos3a

» Sin²Θ+Cos²Θ=1

» Sec²Θ-tan²Θ=1

» Cosec²Θ-Cot²Θ=1

» SinΘ=1/CosecΘ

» CosecΘ=1/SinΘ

» CosΘ=1/SecΘ

» SecΘ=1/CosΘ

» tanΘ=1/CotΘ 

» CotΘ=1/tanΘ

» tanΘ=SinΘ/CosΘ

Formulas of three dimensional solids :(Mensuration)

For a cuboid :  

1 - Volume (V) = l × b × h

2 - Total surface area = 2 (lb × bh × hl )

3 - Diagonal = √ l²× b²×h²

For a cube :

1 - Volume (V) = a³

2 - Total surface area = 6a²

3 - Diagonal = √3 a

For a solid right circular cylinder:

1- Volume (V) = π r²h

2 - Lateral surface area = 2 π r h

3 - Total surface area = 2πr (h + r)

For a hollow right circular cylinder :

1 - Thickness of the material = (R - r)

2 - Volume of the material = π(R² - r²)h

3 - External curved surface area = 2πRh

4 - Internal curved surface area = 2πrh

5 - Total surface area = {2π(R + r) h + 2π(R² - r²)

For a right circular cone:

1 - Slant height = √h²+r²

2 - Volume (V) = 1/3 πr²h

3 - Lateral surface area = πrl

4 - Total surface area = πrl + πr²

For a sphere :

1 - Volume (V) = 4/3 πr³

2 - Surface area = 4πr²

For a spherical shell :

1 - Thickness of the material = ( R - r)

2 - Volume of the material = 4/3 π (R³- r³)

3 - Exterior surface area = 4πR²

4 - Interior surface area = 4πr²

For a hemisphere :

1 - Volume (V) = 2/3πr³

2 - Curved surface area = 2πr²

3 - Total surface area = 3πr²

Distance Formula :

1 - The distance between two points (xₗ , yₗ ) and (x₂ , y₂)

= √(xₗ - x₂)² + (yₗ - y₂)²

= √(difference of x - coordinates )² + ( difference of y - coordinates)²

Middle point of a line segment :

The middle point of a line segment joining the points (xₗ , yₗ ) and (x₂ , y₂ ) has the coordinates

(xₗ +x₂ /2) ,( yₗ + y₂/2)

Section Formula :

If AB is divided at P(x , y) in the ratio m : n , then the coordinates of P are

x = mx₂ + nxₗ / m + n    ,   y = my₂ + nyₗ /m + n

Formulas of equation of straight line :

Equation  of a straight line in the straight intercept  form :

1 - tan𝛉 = mx + c    , where m is slope, which cut off intercept c on the y axis.

2 - The equation of a line passing through (x₁ , y₁ ) and having the slope m is y - y₁ = m(x - x₁)

3 - The equation of the straight line passing through (x₁ , y₁) and (x₂ , y₂ ) is y - y₁ = y₁ - y₂/x₁ - x₂ (x - x₁)