WeTrigonometric identities and formulas are mathematical relationships involving trigonometric functions such as sine, cosine, tangent, secant, cosecant, and cotangent. These identities simplify expressions, solve equations, and prove theorems in geometry and calculus. Key categories include:
1. Reciprocal Identities: Express trigonometric functions in terms of their reciprocals (e.g., ).
2. Pythagorean Identities: Derived from the Pythagorean theorem (e.g., ).
3. Quotient Identities: Relate tangent and cotangent to sine and cosine (e.g., ).
4. Co-Function Identities: Relate functions of complementary angles (e.g., ).
5. Even-Odd Identities: Describe the symmetry of functions (e.g., ).
6. Double Angle and Half Angle Formulas: Simplify trigonometric functions of doubled or halved angles.
7. Sum and Difference Formulas: Simplify expressions for sum or difference of angles (e.g., ).
8. Product-to-Sum and Sum-to-Product Formulas: Convert products into sums and vice versa.
9. Laws of Sines and Cosines: Used to solve triangles, especially non-right triangles.
10. Special Angle Values: Provide specific values for trigonometric functions at common angles (e.g., ).
These formulas are essential tools in mathematics, particularly in solving geometric, algebraic, and calculus-based problems.
