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## Trigonometry Formula Class 10

Trigonometry is that branch of mathematics that deals with the measurement of angles and problems applied with angles.

**Definition of Trigonometry**

The word trigonometry is derived from the words ‘trigonon’ and ‘metron’ which mean triangle and measure respectively. It is the study of the relationship between the sides and angles of a right triangle. Thus it helps to find the measure of unknown dimensions of a right-angled triangle by using formulas and identities based on this relation.

**Meaning of trigonometry:**

Trigonometry = Tri + gono + metry

“Tri” means Triangle

“gono” means Angles

“metry” means Measurement

### Trigonometric Ratio Formula Class 10

There are six basic ratios in trigonometry that help to establish the relationship between the ratio of the sides of a right triangle with the angle.

**SinA = P/H****CosA = B/H****TanA = P/B****CosecA = H/P****SecA = H/B****CotA = B/P**

**Reciprocal Relation of Trigonometric formulas for class 10**

**1. Cosec A = 1/Sin A**

**2. Sin A = 1/Cosec A**

**3. Sec A = 1/Cos A**

**4. Cos A = 1/Sec A**

**5. Cot A = 1/Tan A **

**6. Tan A = 1/Cot A**

**Trigonometric Angles**

Angles | 0° | 30° | 45º | 60° | 90° |

Sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |

Cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |

Tan θ | 0 | 1/√3 | 1 | √3 | ∞ |

Cosec θ | ∞ | 2 | √2 | 2/√3 | 1 |

Sec θ | 1 | 2/√3 | √2 | 2 | ∞ |

Cot θ | ∞ | √3 | 1 | 1/√3 | 0 |

**Trigonometric ratios of complementary Angles**

**1. Sin (90-A) = Cos A**

**2. Cos (90-A) = Sin A**

**3. Tan (90-A) = Cot A**

**4. Cot (90-A) = Tan A**

**5. Sec (90-A) = Cosec A**

**6. Cosec (90-A) = Sec A**

** **

**Some other important class 10 Trigonometry formula**

**1. TanA x CotA = 1**

**2. SinA x CosecA = 1**

**3. CosA x SecA =1**

**4. TanA = SinA/CosA**

**4. CotA = CosA/SinA**

** **

**Trigonometry identity**

An equation involving trigonometric ratios of an** angle** is called a trigonometric identity if it is true for all values of the angle.

Trigonometric identities are useful whenever an expression or equation involves trigonometric functions. Trigonometric identities are true for every value of the variables occurring on both sides of the equation. Geometrically, these identities include some trigonometric functions (e.g. sine, cosine, and tangent) of one or more angles.

**Trigonometric Identity Formula for Class 10**

**1. Sin ^{2}A + Cos^{2}A = 1**

**2. Sec ^{2}A + Tan^{2}A = 1**

**3. Cosec ^{2}A + Sec^{2}A = 1**

**Advance Formula of trigonometry class 10**

**1. Sin (A+B) = SinA x CosB + CosA x SinB**

**2. Sin (A-B) = SinA x CosB – CosA x SinB**

**3. Cos (A+B) = CosA x CosB – SinA x SinB**

**4. Cos (A-B) = CosA x CosB + SinA x SinB**

**5. Tan (A+B) = (TanA + TanB)/(1 – TanA x TanB)**

**6. Tan (A-B) = (TanA – TanB)/(1 + TanA x TanB)**

**7. Sin2A = 2SinACosA**

**OR**

** = 2TanA/(1+Tan ^{2}A)**

** **

**8. Cos2A = Cos ^{2}A – Sin^{2}A **

** OR**

** = 1 – 2Sin ^{2}A**

** OR**

** = 2Cos ^{2}A – 1**

** OR**

** = (1-Tan ^{2}A)/(1+Tan^{2}A)**

** **

** **

**9. Sin3A = 3SinA – 4Sin ^{3}A**

**10. Cos3A = 4Cos ^{3}A – 3CosA**

**11.Tan3A = (3TanA-4Tan ^{2}A)/(1+3Tan^{2}A)**

**12. SinA x Sin2A X Sin4A = ¼ Sin3A**

**13. CosA x Cos2A x Cos4A = ¼ Cos3A**

**14. TanA x Tan2A x Tan4A = Tan3A**

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