# Trigonometry : Complete a Proof Using Sums, Differences, or Products of Sines and Cosines

## Example Questions

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

True or false:

.

False

True

Cannot be determined

False

Explanation:

The sum of sines is given by the formula .

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

True or false: .

False

True

Cannot be determined

False

Explanation:

The difference of sines is given by the formula .

### Example Question #1 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

True or false: .

Cannot be determined

False

True

False

Explanation:

The sum of cosines is given by the formula .

### Example Question #2 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

True or false: .

Cannot be determined

True

False

False

Explanation:

The difference of cosines is given by the formula .

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

Which of the following correctly demonstrates the compound angle formula?

Explanation:

The compound angle formula for sines states that .

### Example Question #6 : Sum, Difference, And Product Identities

Which of the following correctly demonstrates the compound angle formula?

Explanation:

The compound angle formula for cosines states that .

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

Simplify by applying the compound angle formula:

Explanation:

Using the compound angle formula, we can rewrite each half of the non-coefficient terms in the given expression. Given that   and , substitution yields the following:

This is the formula for the product of sine and cosine, .

### Example Question #8 : Sum, Difference, And Product Identities

Simplify by applying the compound angle formula:

Explanation:

Using the compound angle formula, we can rewrite each half of the non-coefficient terms in the given expression. Given that  and , substitution yields the following:

This is the formula for the product of two cosines, .

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

Using  and the formula for the sum of two sines, rewrite the sum of cosine and sine:

Explanation:

Substitute  for :

Apply the formula for the sum of two sines, :

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

Using  and the formula for the difference of two sines, rewrite the difference of cosine and sine: