1, sin(α+β)=sinacosβ+cosasinβ, when β = α, we get sin2α=2sinαcosα.

2.cos(α+β)=cosacosβ-sinasinβ。 When β = α, cos2α=2cos? α- 1= 1-2sin？ α。

3, use α generation 2α, cosα=2cos? α/2- 1= 1-2sin？ α/2 can be obtained by deformation, sinα/2=√( 1-cosα)/2, cosα/2=√( 1+cosα)/2, which can be obtained by bidirectional division, and tan (α/2) = √ (1).

Full-angle formula and half-angle formula are formulas of trigonometric functions commonly used in mathematics, which are used to calculate the trigonometric function value of angles. Full-angle formula includes sine (sin), cosine (cos) and tangent (tan), and half-angle formula is derived from full-angle formula.

The relationship between half angle and full angle:

Full angle and half angle are relative concepts, and full angle is the sum of two half angles. Full angle: a full angle is equal to two half angles, that is, 180 degrees. Half-angle: Half-angle is equal to half of the full angle, that is, 90 degrees. In mathematics and physics, full angle and half angle are often used to describe the size of angle.

For example, in trigonometric functions, sinα represents the sine value of α and cosα represents the cosine value of α. Similarly, tanα represents the tangent value of α. The half-angle formula is derived from the full-angle formula. For example, sin(α/2) represents the sine value of half α, cos(α/2) represents the cosine value of half α, and tan(α/2) represents the tangent value of half α.