Half angle formula.

tan(α/2)= sinα/( 1+cosα)=( 1-cosα)/sinα.

Double angle formula.

tan2α=(2tanα)/( 1-tanα^2)。

Power reduction formula.

tan^2(α)=( 1-cos(2α)/( 1+cos(2α)。

General formula.

tanα=2tan(α/2)/.

Sum and difference formula of two angles.

tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ).

tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ).

Sum and difference product formula.

tanα+tanβ= sin(α+β)/cosαcosβ= tan(α+β)( 1-tanαtanβ).

tanα-tanβ= sin(α-β)/cosαcosβ= tan(α-β)( 1+tanαtanβ).

Brief introduction of trigonometric function

Trigonometric function is a kind of transcendental function in elementary function in mathematics. Their essence is the mapping between the set of arbitrary angles and a set of ratio variables. The usual trigonometric function is defined in the plane rectangular coordinate system, and its domain is the whole real number domain.

The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.

Because of the periodicity of trigonometric function, it does not have the inverse function in the sense of single-valued function.

Trigonometric functions have important applications in complex numbers. Trigonometric function is also a common tool in physics.