Trigonometry is the study of relationships that deal with angles, lengths, and heights of 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.

## ** Trigonometric Formulas:**

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

\((Perpendicular)^{2} + (Base)^{2} = (Hypotenuese)^{2}\)

\(\Rightarrow (P)^{2} + (B)^{2} = (H)^{2}\)

The Trigonometric properties are given below:

S.no | Property | Mathematical value |

1 | \(\sin A\) | \(\frac{P}{H}\) |

2 | \(\cos A\) | \(\frac{B}{H}\) |

3 | \(\tan A\) | \(\frac{P}{B}\) |

4 | \(\cot A\) | \(\frac{B}{P}\) |

5 | \(cosec A\) | \(\frac{H}{P}\) |

6 | \(\sec A \) | \(\frac{H}{B}\) |

Relation Between Trigonometric Identities:

S.no | Identity | Relation |

1 | \(\tan A\) | \(\frac{\sin A}{\cos A}\) |

\(\cot A\) | \(\frac{\cos A}{\sin A}\) | |

3 | \(cosec A\) | \(\frac{1}{\sin A}\) |

4 | \(\sec A\) | \(\frac{1}{\cos A}\) |

**Trigonometric Identities:**

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

These were