### All Precalculus Resources

## Example Questions

### Example Question #1 : Use Product/Sum Identities To Express A Sum Or Difference As A Product

Evaluate the following.

**Possible Answers:**

**Correct answer:**

We can use the angle sum formula for sine here.

If we recall that,

,

we can see that the equation presented is equal to

because .

We can simplify this to , which is simply .

### Example Question #1 : Product/Sum Identities

Evaluate the following.

**Possible Answers:**

**Correct answer:**

The angle sum formula for cosine is,

.

First, we see that . We can then rewrite the expression as,

.

All that is left to do is to recall the unit circle to evaluate,

.

### Example Question #2 : Use Product/Sum Identities To Express A Sum Or Difference As A Product

Evaluate the following.

**Possible Answers:**

**Correct answer:**

This one is another angle sum/difference problem, except it is using the trickier tangent identity.

The angle sum formula for tangent is

.

We can see that .

We can then rewrite the expression as , which is .

### Example Question #1 : Product/Sum Identities

Evaluate the following.

**Possible Answers:**

**Correct answer:**

Here we use the double angle identity for sine, which is

.

We can rewrite the originial expression as using the double angle identity.

From here we can calculate that

.

### Example Question #1 : Product/Sum Identities

Evaluate the following expression.

**Possible Answers:**

**Correct answer:**

One of the double angle formuals for cosine is

.

We can use this double angle formula for cosine to rewrite the expression given as the because and .

We can then calculate that

.

### Example Question #1 : Product/Sum Identities

Evaluate the following.

**Possible Answers:**

**Correct answer:**

Here we can use another double angle formula for cosine,

.

Here , and so we can use the double angle formula for cosine to rewrite the expression as

.

From here we just recognize that

.

### Example Question #1 : Use Product/Sum Identities To Express A Sum Or Difference As A Product

Evaluate the following expression.

**Possible Answers:**

**Correct answer:**

Here we can use yet another double angle formula for cosine:

.

First, realize that .

Next, plug this in to the double angle formula to find that

.

Here we recognize that

### Example Question #31 : Trigonometric Identities

Simplify the following. Leave your answer in terms of a trigonometric function.

**Possible Answers:**

**Correct answer:**

This is a quick test of being able to recall the angle sum formula for sine.

Since,

, and here

, we can rewrite the expression as

.