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)

2) From 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

(The cosine above is very important)

sin2A=2sinA*cosA

3) Half-angle just remember this:

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

(4) The power reduction formula can be derived from the cosine of double angle.

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

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

5) Using the above power reduction formula, the following commonly used simplified formulas can be derived.

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

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

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1) Formula for sum and difference of two angles (remember everything written)

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)

2) From 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

(The cosine above is very important)

sin2A=2sinA*cosA

3) Half-angle just remember this:

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

(4) The power reduction formula can be derived from the cosine of double angle.

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

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

5) Using the above power reduction formula, the following commonly used simplified formulas can be derived.

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

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