গণিতের সূত্রাবলি

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. (a-b)³= a³-b³-3ab(a-b)
16. a³+b³= (a+b) (a²-ab+b²)
17. a³+b³= (a+b)³-3ab(a+b)
18. a³-b³ = (a-b) (a²+ab+b²)
19. a³-b³ = (a-b)³+3ab(a-b)
20. (a² + b² + c²) = (a + b + c)² –             2(ab + bc + ca)
21. 2 (ab + bc + ca) = (a + b + c)²     
– (a² + b² + c²)
22. (a + b + c)³ = a³ + b³ + c³ + 3
        (a + b) (b + c) (c + a)
23. a³ + b³ + c³ – 3abc =(a+b+c)(a² 
+ b²+ c²–ab–bc– ca)
24. a3 + b3 + c3 – 3abc =½ (a+b+c) { (a–b)²+(b–c)²+(c–a)²}
25. (x + a) (x + b) = x² + (a + b) x + ab
26. (x + a) (x – b) = x² + (a – b) x – ab
27. (x – a) (x + b) = x² + (b – a) x – ab
28. (x – a) (x – b) = x² – (a + b) x + ab
29. (x+p) (x+q) (x+r) = x³ + (p+q+r) x² + (pq+qr+rp) x +pqr
30. bc (b-c) + ca (c- a) + ab (a – b) = – (b – c) (c- a) (a – b)
31. a² (b- c) + b² (c- a) + c² (a – b) = -(b-c) (c-a) (a – b)
32. a (b² – c²) + b (c² – a²) + c (a² – b²) = (b – c) (c- a) (a – b)
33. a³ (b – c) + b³ (c-a) +c³ (a -b) =- (b-c) (c-a) (a – b)(a + b + c)
34. b²-c² (b²-c²) + c²a²(c²-a²)+a²b²(a²-b²)=-(b-c) (c-a) (a-b) (b+c) (c+a) (a+b)
 35. (ab + bc+ca) (a+b+c) – abc = (a + b)(b + c) (c+a)
36. (b + c)(c + a)(a + b) + abc = (a + b +c) (ab + bc + ca)
ত্রিকোণমিতির সূত্রসমূহ
1. cosec 0 = 1/sin 0
2.sec 0 = 1/cos 0
3. cot 0 = 1/tan 0
4. sin 0 = 1/cosec 0
5. cos 0 = 1/sec 0
6. tan 0 = 1/cot 0
7. sin0 =1/cosec0 
8. cosec0 =1/sin0
9. cos0 =1/sec0 
10. sec0 =1/cos0
11. tan0 =1/cot0
12. cot0 =1/tan0
13. sin²0 + cos²0= 1
14. sin²0 = 1 – cos²0
15. cos²0 = 1- sin²0
16. sec²0 – tan²0 = 1
17. sec²0 = 1+ tan²0
18. tan²0 = sec²0 – 1
19. cosec²0 – cot²0 = 1
20. cosec²0 = cot²0 + 1
21. cot²0 = cosec²0 – 1
22. sin (A + B) = sin A cos B + cos A sin B
23. sin (A 0 B) = sin A cos B – cos A sin B
24. cos (A + B) = cos A cos B – sin A sin B
25. cos (A – B) = cos A cos B + sin A sin B
26. tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)]
27. tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]
28. sin2A = 2sinA . cosA 
               = [2tan A/(1+tan2 A)]
29. cos2A = cos2A–sin2A 
                = [(1-tan2 A) / (1+tan2 A)]
30. cos2A = 2cos2A01 
                = 1–2sin2A
31. tan(2x) = [2tan(x)]/ [1-tan2(x)]
32. sec (2x) = sec2 x/(2-sec2 x)
33. cos (2x) = (sec x. cos x)/2
34. Sin 3x = 3sin x – 4sin3x
35. Cos 3x = 4cos3x-3cos x
36. Tan 3x = [3tanx-tan3x]/[1-3tan2x]
37. sin x sin y = 1/2 [cos(x–y)- cos(x+y)]
38. cos x cos y = 1/2[cos(x–y) + cos(x+y)]
39. sin x cos y = 1/2[sin(x+y) + sin(x-y)]
40. cos x sin y = 1/2[sin(x+y) – sin(x-y)]
41. sin C + sin D = 2 sin [(C+D)/2] cos [(C-D)/2]
42. sin C – sin D = 2 cos [(C+D)/2] sin [(C-D)/2]
43. cos C + cos D = 2 cos [(C+D)/2] cos [(C-D)/2]
44. cos C – cos D = -2 sin [(C+D)/2] sin [(C-D)/2]