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

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry