Precalculus : Use Product/Sum Identities to Express a Sum or Difference as a Product

Example Questions

Example Question #221 : Pre Calculus

Evaluate the following.       Explanation:

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 #2 : Product/Sum Identities

Evaluate the following.       Explanation:

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

Evaluate the following.       Explanation:

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.       Explanation:

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 #5 : Product/Sum Identities

Evaluate the following expression.       Explanation:

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.       Explanation:

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 #231 : Pre Calculus

Evaluate the following expression.       Explanation:

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 #1 : Product/Sum Identities

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

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 .

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