Sin60.cos30+sin30.cos60
=√3/2 ×√3/2 + 1/2 ×1/2
=√3×√3/2×2 + 1×1/2×2
=3/4 + 1/4
=3+1/4
=4/4
=1

Introduction to Trigonometry
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right-angled triangles. It is essential for various fields such as physics, engineering, and architecture.
Basics of Trigonometric Ratios
- Sine (sin): Ratio of the opposite side to the hypotenuse.
- Cosine (cos): Ratio of the adjacent side to the hypotenuse.
- Tangent (tan): Ratio of the opposite side to the adjacent side.
These ratios are fundamental in solving problems involving angles and sides of triangles.
Applications in Real Life
- Navigation: Trigonometry helps in calculating distances and angles when navigating with maps or GPS.
- Architecture: It is used to calculate structural loads and angles for building designs.
- Astronomy: Helps in determining distances of stars and planets from Earth.
Understanding Trigonometric Identities
Trigonometric identities are equations that involve trigonometric functions and hold true for all values of the involved variables. Some key identities include:
- Pythagorean Identity: sin²A + cos²A = 1
- Angle Sum and Difference Identities: Useful in simplifying expressions involving the sum or difference of angles.
Conclusion
Understanding trigonometry is crucial for solving various mathematical problems and applying them in real-world situations. Mastery of trigonometric ratios and identities will empower students to tackle advanced topics in mathematics confidently.