Trigonometry is one of the most important chapters in Mathematics for JEE and plays a key role in Physics for NEET as well. Many questions in exams are directly based on formulas, so having a strong command over trigonometric formulas can significantly boost your score.
In this blog, we have compiled all the important trigonometry formulas in one place for quick revision and better understanding.
1. Basic Trigonometric Ratios
For a right-angled triangle:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
Other ratios:
cosec θ = 1 / sin θ
sec θ = 1 / cos θ
cot θ = 1 / tan θ
2. Important Trigonometric Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
3. Values of Trigonometric Ratios (Important Angles)
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | Not Defined |
| cosec θ | Not Defined | 2 | √2 | 2/√3 | 1 |
| sec θ | 1 | 2/√3 | √2 | 2 | Not Defined |
| cot θ | Not Defined | √3 | 1 | 1/√3 | 0 |
4. Complementary Angle Formulas
sin (90° – θ) = cos θ
cos (90° – θ) = sin θ
tan (90° – θ) = cot θ
cot (90° – θ) = tan θ
sec (90° – θ) = cosec θ
cosec (90° – θ) = sec θ
5. Compound Angle Formulas
sin (A + B) = sin A cos B + cos 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
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)
6. Double Angle Formulas
sin 2A = 2 sin A cos A
cos 2A = cos²A – sin²A
= 2cos²A – 1
= 1 – 2sin²A
tan 2A = 2tan A / (1 – tan²A)
7. Triple Angle Formula
sin 3A = 3sin A – 4sin³A
cos 3A = 4cos³A – 3cos A
8. Half Angle Formulas
sin²(A/2) = (1 – cos A)/2
cos²(A/2) = (1 + cos A)/2
tan(A/2) = sin A / (1 + cos A)
= (1 – cos A) / sin A
9. Product to Sum Formulas
sin A sin B = ½ [cos(A – B) – cos(A + B)]
cos A cos B = ½ [cos(A – B) + cos(A + B)]
sin A cos B = ½ [sin(A + B) + sin(A – B)]
10. Sum to Product Formulas
sin A + sin B = 2 sin[(A+B)/2] cos[(A–B)/2]
sin A – sin B = 2 cos[(A+B)/2] sin[(A–B)/2]
cos A + cos B = 2 cos[(A+B)/2] cos[(A–B)/2]
cos A – cos B = –2 sin[(A+B)/2] sin[(A–B)/2]
11. Important Tips for Students
Conclusion
Trigonometry becomes very easy if your formulas are strong. Most students lose marks not because they don’t understand the concept, but because they forget formulas during exams.
Make it a habit to revise these formulas regularly and practice questions consistently. This will help you improve speed, accuracy, and confidence in JEE and NEET exams.
Want more such quick revision notes and one-shot lectures?
Join TPLIVE KOTA for JEE & NEET preparation
Get Formula Sheets + Doubt Solving Sessions
Access Recorded + Live Classes
Visit: www.tplivekota.com
TPLIVE KOTA | Learn. Practice. Live Success.
Did you come here for something in particular or just general fiber-bashing? And blowing into
New Posts
Total Visitors
New Subscribers
Blog Read
