Related knowledge:
All Tan's recipes are:
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).