# Precalculus : Sum and Difference Identities

## Example Questions

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### Example Question #1 : Sum And Difference Identities

According to the trigonometric identities,

Explanation:

The trigonometric identity , is an important identity to memorize.

Some other identities that are important to know are:

### Example Question #2 : Sum And Difference Identities

Use the sum or difference identity to find the exact value:

Explanation:

Again, here we break up the 165 into  and solve using the sin identity:

### Example Question #1 : Sum And Difference Identities

Is the following equation an identity?

It cannot be determined from the given information.

Yes it is an identity.

No it is not an identity.

No it is not an identity.

Explanation:

and so this is again not an identity

### Example Question #1 : Sum And Difference Identities

Is the following equation an identity? ?

Yes it is an identity

The question cannot be answered based on the information provided.

No it is not an identity

No it is not an identity

Explanation:

Therefore, this is not an identity.

### Example Question #5 : Sum And Difference Identities

Use the sum or difference identity to find the exact value:

Explanation:

Using the identity, we can break up the 255 into and then solve:

### Example Question #1 : Sum And Difference Identities

Is the following equation an identity?

No it is not an identity.

It cannot be determined from the given information.

Yes it is an identity.

No it is not an identity.

Explanation:

and due to this inequality, this is not an identity

### Example Question #7 : Sum And Difference Identities

Use the sum or difference identity to find the exact value:

Explanation:

Using the identity, we can break up the  into  and then solve:  and so the correct answer is .

### Example Question #1 : Sum And Difference Identities

Is the following equation an identity?

The answer cannot be determined from the information provided.

Yes it is an identity

No it is not an identity

No it is not an identity

Explanation:

Due to this inequality, this is not an identity.

### Example Question #9 : Sum And Difference Identities

Use the sum or difference identity to find the exact value of .

Explanation:

Here we break up the  into  and solve using the sin identity:  and so here the credited answer is .

### Example Question #10 : Sum And Difference Identities

Evaluate the exact value of: