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Today we teach all important math formulas
Which is used in Mostly mathematics Question.
Here is list of mathematics formulae:✅✅
Content list:-
Algebra formula
Trigonometry formula
Algebra
1. (a²-b²) = (a + b)(a - b)
2. (a4- b4) = (a² + b²)(a² - b²) = (a² + b²)(a + b)(a - b)
.3 (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
4.(a³-b³)= (a-b) (a²+ab+b²)
5. (a⁴-b⁴)=(a²+ b²+ ab)(a²+b²-ab)
1. (a + b)² a² + 2ab + b²
2. (a - b)² = a² - 2ab + b²
Note: √a² - 2ab + b² when b > a. = (a - b) when a > band (b - a)
3. (a + b)² = (a - b)² + 4ab
4. (a - b)² = (a + b)²-4ab
5. (a + b)² + (a - b)² = 2(a² + b²)
6. (a + b)²-(a - b)² = 4ab
7.
[(a+b)² + (a−b)²]/a²+b²
= 2
8. [(a+b)²-(a−b)² ]/ ab = 4
9. (a + b)³ = a³ + b³ + 3ab(a + b)
10. (a - b)³ = a³-b³ + 3ab(a - b)
11. a³ + b3 = (a + b)³ - 3ab(a + b)
12. a³ -b³ = (a - b)³ + 3ab(a -b)
13. (a + b)³ + (a - b)³ = 2a(a² + 3b²)
14. (a + b)³ (a - b)³ = 2b(b² + 3a²)
15. (a²-b²) = (a + b)(a - b)
16 (a + b)³ + (a - b)³ = 2a(a² + 3b²)
17.(a + b)³ (a - b)³ = 2b(b² + 3a²)
18.(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
19. a³ + b³ + c³ - 3abc = (a + b + c)(a²+ b²+c²-ab-bc-ca)
If (a + b + c) = 0 then a³ + b³ + c³ = 3abc And a = b = c then also a³ + b³ + c³ = 3abc
20. a³ + b³ + c³ − 3abc = (a + b + c)[(a - b)² + (b − c)² + (c − a)²]
21.(a² + b² + c² − ab — bc – ca) = 1/2[(a−b)² + (b-c)² + (c-a)²]
22 👍 IF (x + 1/x) = a, then (x² + 1 = (a² − 2)
X²+ 1⁄X²= a²-2
X- 1/X = √(a²-4)
X³+1/X³ = a³-3a
X⁴+1/X⁴ =[( X² +1/X²)]²-2 = (a²-2)²-2= a⁴+4-4a²-2= a⁴-4a²+2
X⁵+ 1/X⁵ =(X³+1/X³ )(X²+ 1⁄X²) -(X+1/X) ={a³-3a}{a²-2} - (a)
If ( X-1/X)=A
X³- 1/X³ = A³+3A
7. a³ − b³ = (a − b)(a² + ab + b²)
8. a³+ b³ = (a + b)(a² − ab + b²)
9. aⁿ− bⁿ= (a − b)(aⁿ⁻¹ +aⁿ⁻¹ b +aⁿ⁻³b² + ··· + bⁿ⁻¹)
10. aⁿ = a.a.a . . . n times
11. aⁱ.aⁿ= aⁱ⁺ⁿ
12. aⁱ ÷aⁿ = aⁱ⁻ⁿ if i>n
= 1 if i = n
= 1
13. (aⁱ)ⁿ= aⁱⁿ= (aⁿ)ⁱ
14. (ab)ⁿ= aⁿ.bⁿ
15. (a/b)ⁿ=aⁿ/bⁿ
16. a⁰= 1 where a ∈ R, a≠0
17. a⁻ⁿ = 1/aⁿ
aⁿ=1/a⁻ⁿ
19. If am = an and a≠ ±1, a ≠ 0 then m = n
20. If aⁿ = bⁿ where n≠0, then a = ±b
21. If √x, √y are quadratic surds and if a + √x = √y, then a = 0 and x = y
22. If √x, √y are quadratic surds and if a+ √x = b+ √y then a = b and x = y
23. If a, n,₁ n₂ are positive real numbers and a ≠ 1, then logₐ(ⁿ₁ⁿ₂) = logₐn₁+logₐn₂
24. If a, m, n are positive real numbers, a ≠ 1, then logₐ(m/n)=logₐm-logₐn
25. If a and m are positive real numbers, a≠ 1 then logₐ mⁿ = n logₐm
26. If o,r, and a, are positive real numbers, a≠ 1, r ≠ 1, then logᵣ o=logₐo/logₐr
Other math formula,:-
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Trigonometry formula:✅✅
Here is all Trigonometry formula image you can download either or see them by double tap on it.
Let ∠ABC = θ (Acute angle of right-angle triangle) Here, AC=
Base (b) BC = Perpendicular (a) AB = Hypotenuse (c) There are
six trigonometric ratios,
Pythagoras theorem:
(a)²+ (b)² = (c)²
angleA= 𝛉
𝐒𝐢𝐧 𝛉 =
𝐏𝐞𝐫𝐩𝐞𝐧𝐝𝐢𝐜𝐮𝐥𝐚𝐫
/𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞
= BC/AB
𝐂𝐨𝐬 𝛉 =
𝐁𝐚𝐬𝐞 /𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞 =AC/AB
𝐓𝐚𝐧 𝛉 =
𝐏𝐞𝐫𝐩𝐞𝐧𝐝𝐢𝐜𝐮𝐥𝐚𝐫 /𝐁𝐚𝐬𝐞 =BC/AC
𝐂𝐨𝐭 𝛉 =
𝐁𝐚𝐬𝐞 /𝐏𝐞𝐫𝐩𝐞𝐧𝐝𝐢𝐜𝐮𝐥𝐚𝐫 =AC/BC
𝐒𝐞𝐜 𝛉 =
𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞 /𝐁𝐚𝐬𝐞 =AB/AC
𝐂𝐨𝐬𝐞𝐜 𝛉 =
𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞 /𝐏𝐞𝐫𝐩𝐞𝐧𝐝𝐢𝐜𝐮𝐥𝐚𝐫= AB/BC
Trigonometry function value:
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