Double angle formula is a very practical formula in trigonometric function. Is to use the trigonometric function of this angle to represent the trigonometric function of the double angle. It can be used to simplify the calculation formula and reduce the number of trigonometric functions in calculation, and it is also widely used in engineering.

What are the double angle formulas?

Double angle formula:

Sin2A=2SinA。 Kosa

cos2a=cosa^2-sina^2= 1-2sina^2=2cosa^2- 1

tan2A=(2tanA)/( 1-tanA^2)

(Note: Sina 2 is the square of Sina 2 (a))

Double angle formula:

sin2α=2sinαcosα

tan2α=2tanα/( 1-tan^2(α))

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

Triple angle formula:

sin3α=4sinα sin(π/3+α)sin(π/3-α)

cos3α=4cosα cos(π/3+α)cos(π/3-α)

tan3α=tana tan(π/3+a) tan(π/3-a)

What is the half-angle formula?

tan(A/2)=( 1-cosA)/sinA = sinA/( 1+cosA)；

cot(A/2)= sinA/( 1-cosA)=( 1+cosA)/sinA。

sin^2(a/2)=( 1-cos(a))/2

cos^2(a/2)=( 1+cos(a))/2

tan(a/2)=( 1-cos(a))/sin(a)= sin(a)/( 1+cos(a))

What are the other formulas of trigonometric function?

Product sum and difference formula:

sinαcosβ=( 1/2)[sin(α+β)+sin(α-β)]

cosαsinβ=( 1/2)[sin(α+β)-sin(α-β)]

cosαcosβ=( 1/2)[cos(α+β)+cos(α-β)]

sinαsinβ=-( 1/2)[cos(α+β)-cos(α-β)]

Sum-difference product formula:

sinα+sinβ= 2 sin[(α+β)/2]cos[(α-β)/2]

sinα-sinβ= 2cos[(α+β)/2]sin[(α-β)/2]

cosα+cosβ= 2cos[(α+β)/2]cos[(α-β)/2]

cosα-cosβ=-2 sin[(α+β)/2]sin[(α-β)/2]

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)