the double angle formula is a very practical type of formula in trigonometric functions. that is to express the trigonometric functions of double angles by the trigonometric functions of proper angles. it can be used to simplify calculation formulas and reduce the number of trigonometric functions in calculations. it is also widely used in engineering.

sinαsinβ=-1/2[cos(α+β)-cos(α-β)]

cosαcosβ=1/2[cos(α+β)+cos(α-β)]

sinαcosβ=1/2[sin(α+β)+sin(α-β)]

cosαsinβ=1/2[sin(α+β)-sin(α-β)]