# Important Trigonometry Formulas to Crack Government Exams

Trigonometry is an important part of any government examinations. Some students have a good command over trigonometry but for some, it is a tough challenge to score full marks. The good thing about preparing this part of the mathematics is that it is very much dependent on the basic formulas. So if you can remember **important trigonometry formulas**, you can perform very well.

### Basic Trigonometry Formulas:

Following are some basic trigonometry formulas, which you can learn and solve questions easily. I hope it will help you a lot.

### Basic Table of Trigonometry

0◦ | 30◦ | 45◦ | 60◦ | 90◦ | |

Sin | 0 | 1/2 | 1/√2 | √3/2 | 1 |

Cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |

Tan | 0 | 1/√3 | 1 | √3 | ∞ |

Cot | ∞ | √3 | 1 | 1/√3 | 0 |

Sec | 1 | 2/√3 | √2 | 2 | ∞ |

Cosec | ∞ | 2 | √2 | 2/√3 | 1 |

### Right Angled Triangle:

SinΘ = P/H CosΘ = B/H

TanΘ = P/B CotΘ = B/P

SecΘ = H/B CosecΘ = H/P

If you find it difficult to learn all above formulas, don’t worry. Actually, you do not need to learn all. If you focus on the structure of the trigonometry, you will reach on some important derivations-

- SinΘ/ CosΘ = TanΘ
- SinΘ is opposite of CosecΘ
- CosΘ is opposite of SecΘ
- TanΘ is opposite of CotΘ

Apply these formulas on the above table and triangle. Now you can easily understand how this table and all these formulas work.

### Advance Trigonometry Formulas:

If you have understood the basic formulas, here are some advance trigonometry formulas to help you-

- sinΘ.cosecΘ = 1
- cosΘ.secΘ = 1
- tanΘ.cotΘ = 1
- sin2Θ+ Cos2Θ = 1 or sin2Θ = 1-cos2Θ or cos2Θ = 1=sin2Θ
- sec2Θ-tan2Θ =1 or sec2Θ = 1+tan2Θ or tan2Θ = sec2Θ-1
- cosec2Θ = cot2Θ-1 or cosec2Θ = 1+cot2Θ or cot2Θ = cosec2Θ-1
- sin(90◦-Θ) = cosΘ
- cos(90◦-Θ) = sinΘ
- tan(90◦-Θ) = cotΘ
- cot(90◦-Θ) = tanΘ
- sec(90◦-Θ) = cosecΘ
- cosec(90◦-Θ) = secΘ
- sin(A+B) = sinA.cosB + cosA.sinB
- sin(A-B) = sinA.cosB – cosA.sinB
- cos(A+B) = cosA.cosB – sinA.sinB
- cos(A-B) = cosA.cosB + sinA.sinB
- tan(A+B) = tanA+tanB / 1-tanAtanB
- tan(A-B) = tanA-tanB / 1+tanAtanB
- cot(A+B) = cotA.cotB-1 / cotA+cotB
- cot(A-B) = cotA.cotB+1 / cotB-cotA
- sin2 Θ = 2sin Θ.cos Θ = 2tan Θ / 1+tan2 Θ
- cos2 Θ = cos2 Θ-sin2 Θ = 2cos2 Θ-1 = 1-2sin2 Θ = 1-tan2 Θ / 1+tan2 Θ
- tan2 Θ = 2tan Θ/ 1-tan2 Θ

So these are some basic and advance formulas for trigonometry. Please share with your friends if you find it helpful. Keep in touch with us for more updates.

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