Compound angle formulae

The following are important trigonometric relationships (it is unlikely that you will need to know how to prove them and they may be given in your formula book- check!):

sin(A + B) = sinAcosB + cosAsinB
cos(A + B) = cosAcosB - sinAsinB
tan(A + B) =    tanA + tanB
                    1 - tanAtanB

To find sin(A - B), cos(A - B) and tan(A - B), just change the + signs in the above identities to -

sin(A - B) = sinAcosB - cosAsinB
cos(A - B) = cosAcosB + sinAsinB
tan(A - B) =    tanA - tanB
                   1 + tanAtanB

Double Angle Formulae
sin(A + B) = sinAcosB + cosAsinB
Replacing B by A in the above formula becomes:
sin(2A) = sinAcosA + cosAsinA
so sin2A = 2sinAcosA

similarly, cos2A = cos²A - sin²A
Replacing cos²A by 1 - sin²A (see Pythagorean identities) in the above formula gives:
cos2A = 1 - 2sin²A
Replacing sin²A by 1 - cos²A gives:
cos2A = 2cos²A - 1

It can also be shown that:
tan2A =     2tanA
             1 - tan²A