In mathematics, use the super textbook (but super easy to use formula) to find out the detailed solution.

Triple angle formula

sin3α=4sinα sin(π/3+α)sin(π/3-α)

cos3α=4cosα cos(π/3+α)cos(π/3-α)

tan3a = tan a tan(π/3+a) tan(π/3-a)

General formula of trigonometric function

sinα=2tan(α/2)/[ 1+tan^2(α/2)]

cosα=[ 1-tan^2(α/2)]/[ 1+tan^2(α/2)]

tanα=2tan(α/2)/[ 1-tan^2(α/2)]

Sum difference product

sinθ+sinφ= 2 sin[(θ+φ)/2]cos[(θ-φ)/2]

sinθ-sinφ= 2cos[(θ+φ)/2]sin[(θ-φ)/2]

cosθ+cosφ= 2cos[(θ+φ)/2]cos[(θ-φ)/2]

cosθ-cosφ=-2 sin[(θ+φ)/2]sin[(θ-φ)/2]

tanA+tanB = sin(A+B)/cosa cosb = tan(A+B)( 1-tanA tanB)

tanA-tanB = sin(A-B)/cosa cosb = tan(A-B)( 1+tanA tanB)

Sum and difference of products

sinαsinβ=-[cos(α+β)-cos(α-β)]/2

cosαcosβ=[cos(α+β)+cos(α-β)]/2

sinαcosβ=[sin(α+β)+sin(α-β)]/2

cosαsinβ=[sin(α+β)-sin(α-β)]/2

The above is what I used in high school, and the rest is basically useless.