How to convert cos and sin?

The conversion formula of sin and cos is the relationship between double angle and half angle, and the conversion formula is as follows:

1, double angle conversion formula:

sin2α=2sinαcosα

cos2α=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)？

2. From the double-angle formula, we can continue to derive the half-angle conversion formula:

sin^2(α/2)=( 1-cosα)/2

cos^2(α/2)=( 1+cosα)/2

Other information of cos formula:

It is a periodic function with a minimum positive period of 2π. When the independent variable is 2kπ(k is an integer), the maximum value of the function is1; When the independent variable is (2k+ 1)π, the function has a minimum value of-1, and the cosine function is an even function, and its image is symmetrical about y axis.

Using cosine theorem, we can solve the following two kinds of problems about triangles:

(1) Given three sides, find three angles.

(2) Knowing the angles between two sides and them, find the third side and the other two angles.