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)

Properties of trigonometric functions:

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 accordingly. This ratio is called the tangent of angle A, and is written as tanA, that is, tanA= the opposite side of angle A/the adjacent side of angle A. ..

Similarly, in RT△ABC, if the acute angle A is determined, the ratio of the opposite side to the hypotenuse of the angle A is determined accordingly. This ratio is called sine of angle A, and is recorded as sinA, that is, sinA= the opposite side of angle A/the hypotenuse of angle A. ..

Similarly, in RT△ABC, if the acute angle A is determined, the ratio of the adjacent side to the hypotenuse of the angle A is determined accordingly. This ratio is called cosine of angle A, and it is recorded as cosA, that is, cosA= adjacent side of angle A/hypotenuse of angle A. ..