Trigonometry Formulas for JEE Main 2025 - Download PDF

A list of Trigonometry Formulas for JEE Main 2025 is handy during the last-minute revision before the exam. Trigonometry is an important chapter in the JEE Main Mathematics syllabus and carries a weightage of 3.3%.

Trigonometry Formulas for JEE Main 2025: PDF

Trigonometry constitutes an important part of the Mathematics syllabus in the JEE Main 2025 examination. Trigonometry deals with triangles and the relationship between the sides of a triangle and its angles. Shared below is a PDF containing all the formulas in Trigonometry and are crucial for the JEE Main examination: 

Trigonometry Formulas for JEE Main

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Also Check: JEE Main 2025 Important Formulas

Chapter Wise Trigonometry Formulas for JEE Main 2025

The most important formulas of trigonometry have been shared below:

1. sin θ = Opposite Side / Hypotenuse
2. cos θ = Adjacent Side / Hypotenuse
3. tan θ = Opposite Side / Adjacent Side
4. sec θ = Hypotenuse / Adjacent Side
5. cosec θ = Hypotenuse / Opposite Side
6. cot θ = Adjacent Side / Opposite Side
7. cosec θ = 1/sin θ
8. sec θ = 1/cos θ
9. cot θ = 1/tan θ
10. sin θ = 1/cosec θ
11. cos θ = 1/sec θ
12. tan θ = 1/cot θ
13. sin (π/2 – A) = cos A
14. cos (π/2 – A) = sin A
15. sin (π/2 + A) = cos A
16. cos (π/2 + A) = – sin A
17. sin (3π/2 – A) = – cos A
18. cos (3π/2 – A) = – sin A
19. sin (3π/2 + A) = – cos A
20. cos (3π/2 + A) = sin A
21. sin (π – A) = sin A
22. cos (π – A) = – cos A
23. sin (π + A) = – sin A
24. cos (π + A) = – cos A
25. sin (2π – A) = – sin A
26. cos (2π – A) = cos A
27. sin (2π + A) = sin A
28. cos (2π + A) = cos A
29. sin(90°−x) = cos x
30. cos(90°−x) = sin x
31. tan(90°−x) = cot x
32. cot(90°−x) = tan x
33. sec(90°−x) = cosec x
34. cosec(90°−x) = sec x
35. sin(x + y) = sin(x)cos(y) + cos(x)sin(y)
36. cos(x + y) = cos(x)cos(y) – sin(x)sin(y)
37. sin(x – y) = sin(x)cos(y) – cos(x)sin(y)
38. cos(x – y) = cos(x)cos(y) + sin(x)sin(y)
39. tan(x + y) = (tan x + tan y) / {1 – (tanx.tany)}
40. tan(x - y) = (tan x - tan y) / {1 + (tanx.tany)}
41. cos(2x) = 2cos2(x)−1 = 1–2sin2(x)
42. sin (2x) = 2sin(x).cos(x) = 2 tan(x)/(1 + tan2x)
43. cos (2x) = cos2x – sin2x = (1 - tan2x)/(1 + tan2x)
44. tan (2x) = 2tan(x)/(1 - tan2x)
45. sec (2x) = sec2x / (2 - sec2x )
46. cosec (2x) = sec(x).cosec(x) / 2
47. Sin 3x = 3sin(x) – 4sin3x
48. Cos 3x = 4cos3x-3cos(x)
49. tan (3x) = {3tan(x) – tan3x}/(1 – 3tan2x)
50. sin-1 (–x) = – sin-1 x
51. cos-1 (–x) = π – cos-1 x
52. tan-1 (–x) = – tan-1 x
53. cosec-1 (–x) = – cosec-1 x
54. sec-1 (–x) = π – sec-1 x
55. cot-1 (–x) = π – cot-1 x
56. Sin(x).cos(y) = {sin(x+y) + sin(x-y)} / 2
57. Cos(x).cos(y) = {cos(x+y) + cos(x-y)} / 2
58. Sin(x).sin(y) = {cos(x-y) - cos(x+y)} / 2
59. Sin(x) + sin(y) = 2 sin {(x+y)/2} cos{(x-y)/2}
60. Sin(x) - sin(y) = 2 cos {(x+y)/2} sin{(x-y)/2}
61. cos(x) + cos(y) = 2 cos {(x+y)/2} cos{(x-y)/2}
62. cos(x) - cos(y) = -2 sin {(x+y)/2} sin{(x-y)/2}
63. Sin (x/2) = ± √{(1-cos x) / 2}
64. Cos (x/2) = ± √{(1+cos x) / 2}
65. tan (x/2) = √{(1-cos x)/(1+cos x)} = (1 – cos x)/sin(x)

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Basic Trigonometric Table

It is crucial to remember the trigonometric values both in terms of radian and in degrees. The most common formulas based on angles in trigonometry have been provided in the table below:

Angles (Radian)	0	π/6	π/4	π/3	π/2	π	3π/2	2π
Angles (Degrees)	0	30	45	60	90	180	270	360
sin	0	1/2	1/2	3/2	1	0	-1	0
cos	1	3/2	1/2	1/2	0	-1	0	1
tan	0	1/3	1	3	∞	0	∞	0
sec	∞	3	1	1/ 3	0	∞	0	∞
cosec	∞	2	2	3/2	1	∞	-1	∞
cot	1	2/3	2	1/2	∞	-1	∞	1

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