Maths Formulas for Class 11

Sets Formula

A set is a collection of elements. Now, these elements can be anything. Also, it can be a finite set as well as an infinite set. 

1. The union of two sets X and Y can be denoted as X ∪ Y

2. The difference or intersection of two sets X and Y as X ⋂ Y

3. The complement of X is denoted by X’

4. (i)  ( X ∪ Y )’ = X’ ⋂ Y’

(ii) ( X ⋂ Y )’ = X’ ∪ Y’

5. If (  X ⋂ Y ) = Φ,  then n( X ∪ Y ) = n(A) + n(B) 

6.  (  X ∪ Y ) = Φ, then n (  X ∪ Y ) = n(A) + n(B) - n(A ⋂ B)

Relations and Functions Formula

Formulas important in relations and functions chapter are:

1.  A x B = { (a, b) : a є A, b є  B }

2. If ( p, q ) = ( s, t ) = then p = s and q =  t.

3. If n ( X ) = a and x ( Y ) = b, then n ( X x Y ) = x * y.

4. X x Φ = Φ.

5. The cartesian product: X x Y ≠ Y x X

6. A function f ( x ) from set X to set Y has on relation type where elements of set X have only one image in Y. Therefore, f ( x ) = y or f: X ➝ Y.

7. If function f: A ➝ R and g: A ➝ R, then:

• ( f + g ) ( x ) = f ( x ) + g ( x ), x Є A 

• ( f - g ) ( x ) = f ( x ) - g ( x ), x Є A 

• ( f . g ) ( x ) = f ( x ) . g ( x ), x Є A 

• ( k f) (x) = k (f ( x ) ),  x Є A , k is a number.

• f/g ( x ) = f(x)/g(x), x Є A , g ( x ) ≠ 0

Trigonometric Functions Formula

1. Radius Measure = (π/180) x (Degree Measure)

2. Degree Measure = (180/π) x (Radian Measure)

3. Cos2 y + sin2 y = 1

4. 1 + tan2 y = sec2 y

5. 1 + cot2 y = cosec2 y

6. cos(2nπ + y) = cos y

7. sin(2nπ+ y) = sin y

8. sin ( π- y ) = -sin y

9. cos (π - y ) = - cos y 

10. cos ( (π/2) - y ) = sin y

11. sin ( (π/2) - y ) = cos y

12. sin ( y + x )  = sin y * cos  x + sin x * cos y

13. sin ( y - x )  = sin y * cos  x - sin x * cos y

14. cos ( y + x )  = cos y * cos  x - sin x * sin y

15. cos ( y - x )  = cos y * cos  x + sin x * sin y

16. cos ( (π/2) + y ) =  - sin y

17. sin ( (π/2) + y ) =  - cos y

18. cos(π- y) = - cos y

19. sin (π - y) = sin y

20. cos(π + y) = cos y

21. sin (π + y) = - sin y

22. cos( 2π - y) = - cos y

23. sin ( 2π - y) = - sin y

24. tan (x + y) = (tan x + tan y)/(1 - tan x tan y)

25. tan (x - y) = (tan x - tan y)/(1 + tan x tan y)

26. cot (x + y) = (cot x cot y - 1)/(cot y - cot x)

27. cot (x - y) = (cot x cot y + 1)/(cot y - cot x)

28. Cos 2y = cos2 y - sin2 y = 2 cos2 y - 1 = 1 - 2 sin2 y =  (1 - tan²y)/(1 + tan²y)

29. sin 2y = 2 sin y : cos y =  (2 tan y) (1 + tan²y)

30. sin 3y = 3 sin y - 4 sin3 y

31. tan 3x = (3 tan x - tan³y)/(1 - 3  tan²y)

32. cos x + cos y = 2 cos (x + y)/2 cos (x - y)/2

33. cos x -  cos y =  - 2 sin (x + y)/2 sin(x - y)/2

34. sin x + sin y = 2 sin (x + y)/2 cos (x - y)/2

35. sin x - sin y = 2 cos (x + y)/2 sin (x - y)/2

36. 2 cos x cos y = cos ( x + y ) + cos ( x - y )

37. - 2 sin x sin y = cos ( x + y ) - cos ( x - y )

38. 2 sin x cos y = sin ( x + y ) + sin ( x - y )

39. 2 cos x sin y = sin ( x + y ) - sin ( x - y )

40. sin y = 0; gives y = nπ, where n Є Z

41. cos y = 0; gives y = (2n + 1) π/2, where n Є Z

42. 𝑠𝑖𝑛 𝑥 = 𝑠𝑖𝑛 𝑦; gives x = 𝑛𝜋 + ( - 1 )n y, where n Є Z

43. 𝑐𝑜𝑠 𝑥 = 𝑐𝑜𝑠 𝑦; gives 𝑥 = 2𝑛𝜋 ± 𝑦, where n Є Z

44. Tan x = tan y y; gives x = n𝜋 + y, where n Є Z