Tg should be tan, tangent function, tg is the expression in the old textbook, and now it is generally written as tan.

Tangent theorem: (a+b)/(a-b) = tan ((α+β)/2)/tan ((α-β)/2)

tanA tanB tan(A+B)+tanA+tan B- tan(A+B)= 0

Exponential representation of trigonometric functions in higher algebra (easily obtained from Taylor series);

sinx=[e^(ix)-e^(-ix)]/(2i)

cosx=[e^(ix)+e^(-ix)]/2

tanx=[e^(ix)-e^(-ix)]/[ie^(ix)+ie^(-ix)]

tanA tanB= 1

Extended data:

In Rt△ABC, if the acute angle A is determined, then the ratio of the opposite side to the adjacent side of the angle A is determined. This ratio is called the tangent of angle α, and is written as tanA. That is, the opposite side of tanA = the adjacent side of ∠ a/∠ a.

Trigonometric function of sum and difference of two angles;

cos(α+β)=cosα cosβ-sinα sinβ

cos(α-β)=cosα cosβ+sinα sinβ

sin(α β)=sinα cosβ cosα sinβ

tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)

tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)

Baidu Encyclopedia-Tangent Function