# Precalculus : Sum and Difference Identities For Tangent

## Example Questions

### Example Question #1 : Trigonometric Identities

In the problem below, and .

Find

.

Explanation:

Since and is in quadrant I, we can say that and and therefore:

So
.

Since and is in quadrant I, we can say that and and therefore:

.

So

Using the tangent sum formula, we see:

### Example Question #2 : Trigonometric Identities

In the problem below, and .

Find

.

Explanation:

Since and is in quadrant I, we can say that and and therefore:

So .

Since and is in quadrant I, we can say that and and therefore:

So .

Using the tangent sum formula, we see:

### Example Question #1 : Trigonometric Identities

Given that and , find .

Explanation:

Jump straight to the tangent sum formula:

From here plug in the given values and simplify.

### Example Question #4 : Trigonometric Identities

Which of the following expressions best represents ?

Explanation:

Write the identity for .

Set the value of the angle equal to .

Substitute the value of  into the identity.