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 |

sin^{2} A + cos^{2} A = 1 |

1+tan^{2} A = sec^{2} A |

1+cot^{2} A = cosec^{2} 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)=cos
^{2}A–sin^{2}B=cos^{2}B–sin^{2}A - sin(A+B) sin(A–B) = sin
^{2}A–sin^{2}B=cos^{2}B–cos^{2}A - sinA+sinB = 2 sin (A+B)/2 cos (A-B)/2

**Formulas for twice of the angles:**

- sin2A = 2sinA cosA = [2tan A /(1+tan
^{2}A)] - cos2A = cos
^{2}A–sin^{2}A = 1–2sin^{2}A = 2cos^{2}A–1= [(1-tan^{2}A)/(1+tan^{2}A)] - tan 2A = (2 tan A)/(1-tan
^{2}A)

**Formulas for thrice of the angles:**

- sin3A = 3sinA – 4sin
^{3}A - cos3A = 4cos
^{3}A – 3cosA - tan3A = [3tanA–tan
^{3}A]/[1−3tan^{2}A]

**Also check:**

Only want useful formula of PCM

Please visit: https://byjus.com/formulas/

these all are useful formula of PCM

super

thankyou so much byjus, your quick notes of formulaes helped me alot, thnx again

It’s good thanks byjus

Very useful notes, thanks byjus

Thank you Byju’s. It is very helpful to me

Thanks, guys for making our work easier and a lot more comfortable by posting all the formulas together in one place in a systematic manner

Thank you Byjus. It was really helpful

Very helpful

these are not all

Thanks bijus for the list of formulas

hey how to overcome the fear of phy and chem

try to solve as much questions as you can by yourself, not only for physics chemistry but also for math. you have to deal with it. it looks harder but once you tried to solve you’ll see that these are not much harder. best of luck buddy.

Thank you byju’s your list of formula helped me a lot thankx alot

Thanks but if u keep derivation it will be so useful to others and they will not have any confusion but thanx for this

VERY COOL!!!!!!!

THANK YOU SO MUCH BYJUS FOR MAKING OUR WORK EASY AND SIMPLE

Thank you so much

i would like the list of the trignometric identities for class 11

I just want to say thanks for byjus cz it helped me alot for learning

Hii this is useful formula for Math reading

Thank you so much byjus

Thank u so much😊

thanks for providing all the important formulas of Trignometry

Okay that’s a nice plateform for the students