Trigonometry is a branch of mathematics which studies the relationships between angles and lengths of triangles. It is a very important topic of mathematics just like statistics, linear algebra and calculus. In addition to mathematics, it also contributes majorly to engineering, physics, astronomy and architectural design. Trigonometry Formulas for class 11 play a crucial role in solving any problem related to this chapter. Also, check Trigonometry For Class 11 where students can learn notes, as per the CBSE syllabus and prepare for the exam.
List of Class 11 Trigonometry Formulas
Here is the list of formulas for Class 11 students as per the NCERT curriculum. All the formulas of trigonometry chapter are provided here for students to help them solve problems quickly.
| Trigonometry Formulas |
| sin(−θ) = −sin θ |
| cos(−θ) = cos θ |
| tan(−θ) = −tan θ |
| cosec(−θ) = −cosecθ |
| sec(−θ) = sec θ |
| cot(−θ) = −cot θ |
| Product to Sum Formulas |
| sin x sin y = 1/2 [cos(x–y) − cos(x+y)] |
| cos x cos y = 1/2[cos(x–y) + cos(x+y)] |
| sin x cos y = 1/2[sin(x+y) + sin(x−y)] |
| cos x sin y = 1/2[sin(x+y) – sin(x−y)] |
| Sum to Product Formulas |
| sin x + sin y = 2 sin [(x+y)/2] cos [(x-y)/2] |
| sin x – sin y = 2 cos [(x+y)/2] sin [(x-y)/2] |
| cos x + cos y = 2 cos [(x+y)/2] cos [(x-y)/2] |
| cos x – cos y = -2 sin [(x+y)/2] sin [(x-y)/2] |
| Identities |
| sin2 A + cos2 A = 1 |
| 1+tan2 A = sec2 A |
| 1+cot2 A = cosec2 A |
Sign of Trigonometric Functions in Different Quadrants
| Quadrants→ | I | II | III | IV |
| Sin A | + | + | – | – |
| Cos A | + | – | – | + |
| Tan A | + | – | + | – |
| Cot A | + | – | + | – |
| Sec A | + | – | – | + |
| Cosec A | + | + | – | – |
Basic Trigonometric Formulas for Class 11
cos (A + B) = cos A cos B – sin A sin B
cos (A – B) = cos A cos B + sin A sin B
sin (A+B) = sin A cos B + cos A sin B
sin (A -B) = sin A cos B – cos A sin B
Based on the above addition formulas for sin and cos, we get the following below formulas:
- sin(π/2-A) = cos A
- cos(π/2-A) = sin A
- sin(π-A) = sin A
- cos(π-A) = -cos A
- sin(π+A)=-sin A
- cos(π+A)=-cos A
- sin(2π-A) = -sin A
- cos(2π-A) = cos A
If none of the angles A, B and (A ± B) is an odd multiple of π/2, then
- tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)]
- tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]
If none of the angles A, B and (A ± B) is a multiple of π, then
- cot(A+B) = [(cot A cot B − 1)/(cot B + cot A)]
- cot(A-B) = [(cot A cot B + 1)/(cot B – cot A)]
Some additional formulas for sum and product of angles:
- cos(A+B) cos(A–B)=cos2A–sin2B=cos2B–sin2A
- sin(A+B) sin(A–B) = sin2A–sin2B=cos2B–cos2A
- sinA+sinB = 2 sin (A+B)/2 cos (A-B)/2
Formulas for twice of the angles:
- sin2A = 2sinA cosA = [2tan A /(1+tan2A)]
- cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)]
- tan 2A = (2 tan A)/(1-tan2A)
Formulas for thrice of the angles:
- sin3A = 3sinA – 4sin3A
- cos3A = 4cos3A – 3cosA
- tan3A = [3tanA–tan3A]/[1−3tan2A]
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