Sum and difference of two angles:

1、 1cos(α+β)= cosαcosβ-sinαsinβ

2、cos(α-β)=cosα cosβ+sinα sinβ

3、sin(α β)=sinα cosβ cosα sinβ

4、4 tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)

5、tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)

Tangent theorem:

In a plane triangle, the tangent theorem shows that the quotient obtained by dividing the sum of any two sides by the difference between the first side and the second side is equal to the quotient obtained by dividing the tangent of half the sum of the diagonals of these two sides by the tangent of the difference between the diagonals of the first side and the second side.

Franciscus Vieta (Fran &; CcedilOis Viète) once put forward the tangent theorem in his first book on trigonometry, Mathematical Rules Applied to Triangle.

For example, because Chinese people criticized the former Soviet Union and its pedagogy, the tangent theorem was deleted from middle school mathematics textbooks from 65438 to 65438 to 0977. But when there is no computer to help solve triangles, this theorem is easier to use logarithm to calculate projections and other problems than cosine theorem.