Trigonometry is the study of relationships between angles, lengths, and heights of triangles. It includes ratios, function, identities, formulas to solve problems based on it, especially for right-angled triangles. Applications of trigonometry are also found in engineering, astronomy, Physics and architectural design. This chapter is very important as it comprises many topics like Linear Algebra, Calculus and Statistics.

Trigonometry is introduced in CBSE Class 10. It is a completely new and tricky chapter where one needs to learn all the formula and apply them accordingly. Trigonometry Class 10 formulas are tabulated below.

## List of Trigonometric Formulas for 10th

Applying Pythagoras theorem for the given right-angled triangle, we have:

(Perpendicular)^{2}+(Base)^{2}=(Hypotenuse)^{2}

⇒(P)^{2}+(B)^{2}=(H)^{2}

The Trigonometric formulas are given below:

S.no |
Property |
Mathematical value |

1 | sin A | Perpendicular/Hypotenuse |

2 | cos A | Base/Hypotenuse |

3 | tan A | Perpendicular/Base |

4 | cot A | Base/Perpendicular |

5 | cosec A | Hypotenuse/Perpendicular |

6 | sec A | Hypotenuse/Base |

### Reciprocal Relation Between Trigonometric Ratios

S.no |
Identity |
Relation |

1 | tan A | sin A/cos A |

2 | cot A | cos A/sin A |

3 | cosec A | 1/sin A |

4 | sec A | 1/cos A |

### Trigonometric Sign Functions

- sin (-θ) = − sin θ
- cos (−θ) = cos θ
- tan (−θ) = − tan θ
- cosec (−θ) = − cosec θ
- sec (−θ) = sec θ
- cot (−θ) = − cot θ

### Trigonometric Identities

- sin
^{2}A + cos^{2}A = 1 - tan
^{2}A + 1 = sec^{2}A - cot
^{2}A + 1 = cosec^{2}A

### Periodic Identities

- sin(2nπ + θ ) = sin θ
- cos(2nπ + θ ) = cos θ
- tan(2nπ + θ ) = tan θ
- cot(2nπ + θ ) = cot θ
- sec(2nπ + θ ) = sec θ
- cosec(2nπ + θ ) = cosec θ

### Complementary Ratios

**Quadrant I**

- sin(π/2−θ) = cos θ
- cos(π/2−θ) = sin θ
- tan(π/2−θ) = cot θ
- cot(π/2−θ) = tan θ
- sec(π/2−θ) = cosec θ
- cosec(π/2−θ) = sec θ

**Quadrant II**

sin(π−θ) = sin θ

cos(π−θ) = -cos θ

tan(π−θ) = -tan θ

cot(π−θ) = – cot θ

sec(π−θ) = -sec θ

cosec(π−θ) = cosec θ

**Quadrant III**

- sin(π+ θ) = – sin θ
- cos(π+ θ) = – cos θ
- tan(π+ θ) = tan θ
- cot(π+ θ) = cot θ
- sec(π+ θ) = -sec θ
- cosec(π+ θ) = -cosec θ

**Quadrant IV**

- sin(2π− θ) = – sin θ
- cos(2π− θ) = cos θ
- tan(2π− θ) = – tan θ
- cot(2π− θ) = – cot θ
- sec(2π− θ) = sec θ
- cosec(2π− θ) = -cosec θ

### Sum and Difference of Two Angles

- 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)]

### Double Angle Formulas

- 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)

### Thrice of Angle Formulas

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

**Also, check:**

Thank-you

good content

Thanks sir for understanding of TRIGONOMETRY

thnx the notes were absolutely helpful

it was helpful

This is so helpful thank you so much Byjus☺️

Don’t Stop Here Only It would be better If you would Give more formulas in free.

It may become blessing for someone Hence please write down all the formula of trigonometry. I am the teacher of Excellence Public School. If you will do this for poor students so they would be very thankful to you in fact I will be also.

Thankyou Somuch😊😊😊

Sir your thinking is excellent.

https://byjus.com/maths/trigonometric-identities/

My name is Fazil

thank you for the creators of byjus , it is a wonderful app and keep going

Give all formulas

This is so helpful 😊

The content made me Contented and It helped me too.

This is very useful content. If Byju’s present physics chemistry law that will be more better for us.

thank yoou