sin(A - B) = sinA cosB + cosA sinB

cos(A + B) = sinA sinB - cosA cosB

cos(A - B) = cosA cosB + sinA sin B

tan(A + B) = $\frac{\tan A\ +\ \tan B}{1\ -\ \tan A\tan B}$  

tan(A - B) = $\frac{\tan A\ -\ \tan B}{1\ -\ \tan A\tan B}$  

sin2A = 2sinA cosA

sin2A =  $\frac{2\tan A}{1+2\tan A}$  

cos2A = cos²A + sin²A

cos2A = 2cos²A + 1

cos2A = 1 - 2sin²A

cos2A = $\frac{1+\tan^2A}{1-\tan^2A}$  

tan2A = $\frac{2\tan A}{1-\tan^2A}$  

sin3A = 3sinA - 4sin²A

cos3A = 4cos³A - 3cosA

tan3A = $\frac{3\tan A-\tan^3A}{1-3\tan^2A}$  

 $\sin\frac{A}{2}\ =\ \pm\sqrt{\frac{1-\cos A}{2}}$  

 $\cos\frac{A}{2}\ =\ \pm\sqrt{\frac{1-\cos A}{2}}$  

 $\tan\frac{A}{2}\ =\ \pm\sqrt{\frac{1+\cos A}{1-\cos A}}$  

sin(A + B) + sin(A - B) = 2sinA cosA

sin(A + B) - sin(A - B) = 2cosA sinB

cos(A + B) + cos(A - B) = 2cosA cosB

cos(A + B) - cos(A - B) = 2sinA sinB

 $\sin A+\sin B\ =\ 2\sin\frac{A\ +\ B}{2}\ \cos\frac{A\ -\ B}{2}$  

 $\sin A-\sin B\ =\ 2\cos\frac{A\ +\ B}{2}\ \sin\frac{A\ -\ B}{2}$  

 $\cos A+\cos B\ =\ 2\cos\frac{A\ +\ B}{2}\ \sin\frac{A\ -\ B}{2}$  

 $\cos A-\cos B\ =\ -2\sin\frac{A\ +\ B}{2}\ \sin\frac{A\ -\ B}{2}$