Whenever trigonometric functions are involved in an expression or an equation, trigonometric identities are helpful. Identity inequalities found on both sides of an equation are valid for any value. Geometrically, certain functions of one or more angles involve these identities. There are various distinct identities involving the side length as well as the angle of a triangle. The trigonometric identities hold true only for the right-angle triangle.
Sine, cosine, tangent, cosecant, secant, and cotangent, are the six fundamental trigonometric ratios. All these trigonometric ratios are described using the sides of the right triangle like adjacent side, opposite side, and hypotenuse side.
Examples of fundamental trigonometric identities
- Sin θ = 1/Csc θ
- Cos θ = 1/Sec θ
- Tan θ = 1/Cot θ
- Csc θ = 1/Sin θ
- Sec θ = 1/Cos θ
- Cot θ = 1/Tan θ