Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It explores the properties and functions of angles and trigonometric ratios, which are the ratios of the lengths of the sides of a right triangle.

Trigonometry is widely used in various fields such as physics, engineering, architecture, and navigation. It helps in solving problems related to distances, heights, angles, and trajectories. The fundamental trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which represent the ratios of the sides of a right triangle.

By using these trigonometric functions and various trigonometric identities and formulas, trigonometry enables us to calculate unknown angles or side lengths in triangles. It also helps in analyzing periodic phenomena, such as oscillations and waves.

Trigonometry has practical applications in real-world scenarios, such as calculating distances between objects, determining the heights of buildings, designing bridges and structures, and navigating using compasses and GPS systems.

Overall, trigonometry plays a crucial role in understanding and solving problems involving angles and triangles, providing a valuable toolset for a wide range of scientific and practical applications.

Trigonometry is an important topic in mathematics, and here are some key trigonometric formulas for Class 10 students:

**Pythagorean Identities trigonometric formulas:**- sin^2θ + cos^2θ = 1
- tan^2θ + 1 = sec^2θ
- 1 + cot^2θ = cosec^2θ

**Reciprocal Identities trigonometric formulas:**- sinθ = 1/cosecθ
- cosθ = 1/secθ
- tanθ = 1/cotθ

**Co-function Identities trigonometric formulas:**- sin(90° – θ) = cosθ
- cos(90° – θ) = sinθ
- tan(90° – θ) = cotθ

**Angle Sum and Difference Formulas trigonometric formulas:**- sin(A ± B) = sinAcosB ± cosAsinB
- cos(A ± B) = cosAcosB ∓ sinAsinB
- tan(A ± B) = (tanA ± tanB) / (1 ∓ tanAtanB)

**Double Angle Trigonometry Formulas:**- sin2θ = 2sinθcosθ
- cos2θ = cos^2θ – sin^2θ
- tan2θ = (2tanθ) / (1 – tan^2θ)

**Half Angle Trigonometry Formulas:**- sin(θ/2) = ±√[(1 – cosθ) / 2]
- cos(θ/2) = ±√[(1 + cosθ) / 2]
- tan(θ/2) = ±√[(1 – cosθ) / (1 + cosθ)]

These Trigonometry formulas are useful for solving trigonometric problems and understanding the relationships between angles and trigonometric ratios. Remember to practice applying these formulas to gain proficiency in trigonometry.