Also, read |

Trigonometry for class 10 |

Applications of Trigonometry |

Inverse Trigonometric Function |

# Trigonometric formulas:

When you begin solving trigonometry it seems vast one, but it is not what you believe. This chapter is so much easy to solve. In this section, **trigonometric formulas** for class 10, 11, 12 is available. These formula include all **trigonometric ratios, trigonometric identities, trigonometric sign rule, quadrant rule** and some of the value of the trigonometric function of specific degrees.

**Trigonometric formulas list:**

Trigonometric identities are of great use in solving question which covers the major portion of mathematics in class 10, 11 and 12th. The complete **list of trigonometric formula** will help you whenever and wherever you want.

**Trigonometric Ratios:**

Functions |
Value |

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

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

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

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

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

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

**Trigonometric formulas based on relations:**

Functions |
Relations |

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

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

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

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

**Negative sign convention of Trigonometric function:**

The negative sign (-A) has usual meaning in terms of (2π – A).

S.no. |
Function |

1. |
sin(-A) = – sin A |

2. |
cos(-A) = cos A |

3. |
tan(-A) = – tan A |

4. |
cosec(-A) = – cosec A |

5. |
sec(-A) = sec A |

6. |
cot(-A) = – cot A |

**Sign convention in Trigonometry:**

Also, common used function in quadrants:

The sign convention in these quadrant is remembered as

** “All School To College”**

i.e.

- All positive for 1
^{st}quadrant, - Sin and cosec positive for 2
^{nd}quadrant, - Tan and cot positive for 3
^{rd}quadrant, - Cos and sec positive in 4
^{th .}

S.no. |
Value |

1. |
sin(90⁰-A) = cos A |

2. |
cos(90⁰-A) = sin A |

3. |
tan(90⁰-A) = cot A |

4. |
cosec(90⁰-A) = sec A |

5. |
sec(90⁰-A) = cosec A |

6. |
cot(90⁰-A) = tan A |

Revise these trigonometric formulas daily to score better in your board exams as well as for JEE, SSC etc. like competitive examination.

**Trigonometric Identities:**

S.no. |
Identities |

1. |
sin^{2 }A + cos^{2} A = 1 |

2. |
sec^{2 }A – tan^{2} A = 1 |

3. |
cosec^{2 }A – cot^{2 }A = 1 |

**Trigonometric Formula As Product Rule:**

S.no. |
Rules |

1. |
sin (A + B) = sin A cos B + cos A sin B |

2. |
sin (A – B) = sin A cos B – cos A sin B |

3. |
cos (A + B) = cos A cos B – sin A sin B |

4. |
cos (A – B) = cos A cos B + sin A sin B |

5. |
tan (A + B) = \(\frac{tanA + tanB}{1 – tanA\: tanB}\) |

6. |
tan (A – B) = \(\frac{tanA – tanB}{1 + tanA\: tanB}\) |

**Trigonometric Formulas for Double Angle:**

S.no. |
Formulae |

1. |
sin 2A = 2 sin A∙cos A |

2. |
cos 2A = cos^{2}A – sin^{2}A=2cos^{2}A – 1= 1 – 2sin^{2}A |

3. |
tan 2A = \(\frac{2tanA}{1- {tan}^{2}A}\) |

**Trigonometric Formulas for Triple Angle:**

S.no. |
Formulae |

1. |
Sin 3A = 3sinA – 4sin^{3}A |

2. |
Cos 3A = 4cos^{3}A – 3cosA |

3. |
Tan3A = \(\frac{3tanA – {tan}^{3}A}{1- 3{tan}^{2}A}\) |

4. |
Cot3A = \(\frac{{cot}^{3}A – 3cotA}{3{cot}^{2}A – 1}\) |

**Trigonometric product conversion:**

S.no. |
Formulae |

1. |
\(\frac{cos(A – B) – cos(A+B)}{2}\) = sinA.sinB |

2. |
\(\frac{cos(A – B) + cos(A+B)}{2}\) = cosA.cosB |

3. |
\(\frac{sin(A + B) + sin(A – B)}{2}\) = sinA.cosB |

4. |
\(\frac{cos(A + B) + sin(A – B)}{2}\) = cosA.sinB |

**Extended product rule:**

S.no. |
Formulae |

1. |
sinA.sinB = \(\frac{cos\frac{(A + B)}{2}.cos\frac{(A-B)}{2}}{2}\) |

2. |
cosA.cosB = \(\frac{cos\frac{(A + B)}{2}.sin\frac{(A-B)}{2}}{2}\) |

3. |
sinA.cosB = \(\frac{sin\frac{(A + B)}{2}.cos\frac{(A-B)}{2}}{2}\) |

4. |
cosA.sinB = \(\frac{sin\frac{(A + B)}{2}.sin\frac{(A-B)}{2}}{2}\) |

**Trigonometric Half Angle Identities:**

S.no. |
Formulae |

1. |
\(\sin\frac{x}{2}=\pm \sqrt{\frac{1-\cos\: x}{2}}\) |

2. |
\(\cos\frac{x}{2}=\pm \sqrt{\frac{1+\cos\: x}{2}}\) |

3. |
\(\tan(\frac{x}{2}) = \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\) |

4. |
\(\tan(\frac{x}{2}) = \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\) Also, \(\tan(\frac{x}{2}) =\frac{1-\cos(x)}{\sin(x)}\) |

**Trigonometric formulas** will make you easy to solve questions. Keep a bookmark of this site to learn and revise it regularly. **Class 10th trigonometric formula **is here with complete evaluation.

**Trigonometric ratio of some specific angles:**

The trigonometric ratio of 0°, 30°, 45°, 60°, 90° is mentioned below. take a look at it.

∠A |
0⁰ |
30⁰ |
45⁰ |
60⁰ |
90⁰ |

sin A |
0 | \(\frac{1}{2}\) | \(\frac{1}{\sqrt{2}}\) | \(\frac{\sqrt{3}}{2}\) | 1 |

cos A |
1 | \(\frac{\sqrt{3}}{2}\) | \(\frac{1}{\sqrt{2}}\) | \(\frac{1}{2}\) | 0 |

tan A |
0 | \(\frac{1}{\sqrt{3}}\) | 1 | \(\sqrt{3}\) | Not defined |

sec A |
1 | \(\frac{2}{\sqrt{3}}\) | \(\sqrt{2}\) | 2 | Not defined |

cot A |
Not defined | \(\sqrt{3}\) | 1 | \(\frac{1}{\sqrt{3}}\) | 0 |

cosec A |
Not defined | 2 | \(\sqrt{2}\) | \(\frac{2}{\sqrt{3}}\) | 1 |

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