Sum and difference formula of two angles

sin(A+B)=sinAcosB+cosAsinB

sin(A-B)=sinAcosB-sinBcosA？

cos(A+B)=cosAcosB-sinAsinB

cos(A-B)=cosAcosB+sinAsinB

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

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

Secondly, with the above formula, the following double-angle formula can be derived.

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

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

sin2A=2sinA*cosA

Three, half angle just remember this:

Tan(A/2)=( 1-cosA)/ Sina = Sina /( 1+cosA)

Fourthly, the formula of power reduction can be derived from the double angle cosine.

(sinA)^2=( 1-cos2A)/2

(cosA)^2=( 1+cos2A)/2

Five, using the above formula to reduce the power, the following commonly used simplified formulas can be derived.

1-cosA=sin^(A/2)*2

1-sinA=cos^(A/2)*2