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]

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