Trigonometry is a branch of mathematics that deals with the study of triangles and their properties. This includes the relationships between the sides and angles of a triangle. Trigonometry is widely used in various fields such as engineering, physics, and astronomy. Here are some of the formulas related to trigonometry:

Basic Trigonometric Ratios
- Sine: sinθ = opposite/hypotenuse
- Cosine: cosθ = adjacent/hypotenuse
- Tangent: tanθ = opposite/adjacent

Reciprocal Trigonometric Ratios
- Cosecant: cscθ = hypotenuse/opposite
- Secant: secθ = hypotenuse/adjacent
- Cotangent: cotθ = adjacent/opposite

Pythagorean Identity
- sin²θ + cos²θ = 1

Co-Function Identities
- sin(90° - θ) = cosθ
- cos(90° - θ) = sinθ
- tan(90° - θ) = cotθ
- cot(90° - θ) = tanθ
- sec(90° - θ) = cscθ
- csc(90° - θ) = secθ

Angle Sum and Difference Identities
- sin(A ± B) = sinA cosB ± cosA sinB
- cos(A ± B) = cosA cosB ∓ sinA sinB
- tan(A ± B) = (tanA ± tanB)/(1 ∓ tanA tanB)

Double Angle Identities
- sin2θ = 2sinθ cosθ
- cos2θ = cos²θ - sin²θ
- tan2θ = (2tanθ)/(1 - tan²θ)

Half Angle Identities
- sin(θ/2) = ±√[(1 - cosθ)/2]
- cos(θ/2) = ±√[(1 + cosθ)/2]
- tan(θ/2) = ±√[(1 - cosθ)/(1 + cosθ)]

Trigonometry is a fascinating subject that is essential for understanding various concepts in mathematics and other fields. These formulas are just the beginning of what you can explore in trigonometry.