CBSE · Class 11
Trigonometry Formulas for Class 11
All trigonometric identities, compound angle formulas, and standard results for CBSE Class 11 and JEE preparation
Ch 1.Basic Trigonometric Ratios and Identities
| Formula / Relation | Expression |
|---|---|
| sin²θ + cos²θ | sin²θ + cos²θ = 1 |
| 1 + tan²θ | 1 + tan²θ = sec²θ |
| 1 + cot²θ | 1 + cot²θ = cosec²θ |
| tan θ | tan θ = sin θ / cos θ |
| Reciprocal identities | cosec θ = 1/sin θ; sec θ = 1/cos θ; cot θ = 1/tan θ |
Ch 2.Trigonometric Ratios of Standard Angles
| Formula / Relation | Expression |
|---|---|
| sin values | sin 0°=0, sin 30°=½, sin 45°=1/√2, sin 60°=√3/2, sin 90°=1 |
| cos values | cos 0°=1, cos 30°=√3/2, cos 45°=1/√2, cos 60°=½, cos 90°=0 |
| tan values | tan 0°=0, tan 30°=1/√3, tan 45°=1, tan 60°=√3, tan 90°=undefined |
Ch 3.Compound Angle Formulas
| Formula / Relation | Expression |
|---|---|
| sin(A + B) | sin(A + B) = sin A cos B + cos A sin B |
| sin(A − B) | sin(A − B) = sin A cos B − cos A sin B |
| cos(A + B) | cos(A + B) = cos A cos B − sin A sin B |
| cos(A − B) | cos(A − B) = cos A cos B + sin A sin B |
| tan(A + B) | tan(A + B) = (tan A + tan B) / (1 − tan A tan B) |
| tan(A − B) | tan(A − B) = (tan A − tan B) / (1 + tan A tan B) |
Ch 4.Double Angle Formulas
| Formula / Relation | Expression |
|---|---|
| sin 2A | sin 2A = 2 sin A cos A |
| cos 2A — three forms | cos 2A = cos²A − sin²A = 1 − 2sin²A = 2cos²A − 1 |
| tan 2A | tan 2A = 2 tan A / (1 − tan²A) |
Ch 5.Half Angle Formulas
| Formula / Relation | Expression |
|---|---|
| sin²(A/2) | sin²(A/2) = (1 − cos A) / 2 |
| cos²(A/2) | cos²(A/2) = (1 + cos A) / 2 |
| tan(A/2) | tan(A/2) = sin A / (1 + cos A) = (1 − cos A) / sin A |
Ch 6.Sum-to-Product and Product-to-Sum
| Formula / Relation | Expression |
|---|---|
| sin C + sin D | sin C + sin D = 2 sin((C+D)/2) cos((C−D)/2) |
| sin C − sin D | sin C − sin D = 2 cos((C+D)/2) sin((C−D)/2) |
| cos C + cos D | cos C + cos D = 2 cos((C+D)/2) cos((C−D)/2) |
| cos C − cos D | cos C − cos D = −2 sin((C+D)/2) sin((C−D)/2) |
Ch 7.Trigonometric Equations
| Formula / Relation | Expression |
|---|---|
| sin θ = sin α general solution | θ = nπ + (−1)ⁿ α, n ∈ ℤ |
| cos θ = cos α general solution | θ = 2nπ ± α, n ∈ ℤ |
| tan θ = tan α general solution | θ = nπ + α, n ∈ ℤ |
Ch 8.Properties of Triangle (Class 11)
| Formula / Relation | Expression |
|---|---|
| Sine rule | a/sin A = b/sin B = c/sin C = 2R |
| Cosine rule | a² = b² + c² − 2bc cos A |
| Area of triangle | Area = (1/2) ab sin C |
| Hero's formula | Area = √[s(s−a)(s−b)(s−c)] |
Frequently Asked Questions
How many trigonometry formulas are there in Class 11?
Class 11 trigonometry has approximately 40–50 standard formulas: 5 basic identities, 15+ compound/multiple angle formulas, 8 sum-to-product formulas, 3 general solution formulas, and triangle formulas. For JEE, you need all of them. For CBSE board, focus on: basic identities, compound angles, double angles, and half angles.
What is the most important trig formula for JEE?
For JEE, the most critical groups are: (1) all compound angle formulas — sin(A±B), cos(A±B), tan(A±B); (2) double angle formulas — especially the three forms of cos 2A; (3) sum-to-product formulas — frequently tested in JEE Main; (4) inverse trigonometry properties. Master these before moving to other topics.
What is the trick to remember compound angle formulas?
For sin: 'All Silver Tea Cups' — All (sin A cos B), Silver (cos A sin B), Tea (minus/plus). sin(A+B) = sin A cos B + cos A sin B. For cos: 'CoCo SiSi' but reversed sign — cos(A+B) = cos A cos B − sin A sin B (note minus). For tan: fraction with sum/difference on top and 1 ∓ product on bottom.
What is the general solution of a trigonometric equation?
For sin θ = sin α: θ = nπ + (−1)ⁿα. For cos θ = cos α: θ = 2nπ ± α. For tan θ = tan α: θ = nπ + α. The general solution represents all angles that satisfy the equation, since trig functions are periodic. In exams, always express the general solution, then find specific solutions within the given range (like 0 to 2π).
How to study trigonometry for Class 11 efficiently?
Week 1: Memorise all standard values (0°,30°,45°,60°,90°) and basic identities. Week 2: Compound angle formulas with daily practice problems. Week 3: Double, triple, half angle formulas. Week 4: Sum-to-product, general solutions. Use NCERT examples and exercise thoroughly — Class 11 NCERT trig is well-structured. Practice 10 problems daily; speed and accuracy come from volume.
Related resources
Master Class 11 Trigonometry
Expert Maths tutors who build your trigonometry skills from the ground up — essential for Class 12 boards and JEE/NEET preparation.
Find a Class 11 Maths TutorFor reference only. Formulas and information on this page may contain errors or may have been updated since publication. Always verify against your official NCERT textbooks, board-prescribed materials, or the relevant official source before use in exams or assessments. Learnizo is not responsible for any inaccuracies.