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Trigonometric formulas for class 10 are given here for students. Trigonometry is the study of relationships among angles, lengths and heights of triangles. It includes functions identities, ratios and formulas to solve right-angled triangle problems; its applications span across engineering, astronomy, Physics and architectural design among others. This Trigonometry chapter is most important because its covers many topics and many diffrents formulas **for example:** linear algebra, calculus, and statistics.

Trigonometry is introduced into 10 Class CBSE. This chapter is completely new and tricky chapter where one needs to learn all the formulas and apply them accordingly.

## List of Trigonometric Formulas for 10th Class

Knowledge Glow provides all of the essential trigonometry formulas for Class 10 students and makes learning them much easier and faster. Students can learn these formulas from Knowledge Glow and resolve trigonometry-related problems more efficiently.

Class 10 trigonometric formulas for ratios focus primarily on three sides of a right-angled triangle: such as adjacent side or perpendicular, base, and hypotenuse.

**Now,** Apply Pythagoras theorem for the given angled triangle.

(P)2 + (B)2 = (H)2

(Perpendicular)2 + (Base)2 = (Hypotenuse)2

Now let us check the trigonometric ratios (sine, cosine, tangent, secant, cosecant, and cotangent).

## Basic Trigonometric Formulas

The Basic Trigonometric formulas for class 10 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 |

## Relations 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

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

## Triple Angle Formulas

- sin 3A = 3 sinA – 4 sin
^{3}A - cos 3A = 4 cos
^{3}A – 3 cos A - tan 3A = [3 tan A – tan
^{3}A] / [1 − 3 tan^{2}A]