# How to determine of tangent (A – B) and tangent (A + B)

We can use the identity and the identities for sin (*A *+ *B*) and cos (*A *+ *B*) to write identities for tan (*A *+ *B*) and tan (*A *– *B*).

**Tangent of ( A **+

*B*)

Also Read:

We would like to write this identity for tan (*A *+ *B*) in terms of tan *A *and tan *B*. We can do this by dividing each term of the numerator and each term of the denominator by cos *A *cos *B*. When we do this we are dividing by a fraction equal to 1 and therefore leaving the value of the expression unchanged.

**Tangent of ( A **–

*B*)The identity for tan (*A *– *B*) can be derived in a similar manner.

These identities are true for all replacements of *A *and *B *for which and , and for which tan (*A *+ *B*) or tan (*A *– *B*) are defined.

**Also Read : Determine sine ( A – B) and sine ( A + B) of trigonometric**

Example 1:

Use and to show that .

Solution:

.

Example 2:

Use (45° + 120°) = 165° to find the exact value of tan 165°.

Solution:

and , so .

and , so .